hands_on_ml_lecture5_support_vector_machines.ipynb

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    "colab": {
      "name": "05_support_vector_machines.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mshahbaba/lantern-examples/blob/master/hands_on_ml_lecture5_support_vector_machines.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MwOwKb9JRj7U",
        "colab_type": "text"
      },
      "source": [
        "**Chapter 5 – Support Vector Machines**\n",
        "\n",
        "_This notebook contains all the sample code and solutions to the exercises in chapter 5._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9-kEVXsVRj7V",
        "colab_type": "text"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2PtKE6NRj7W",
        "colab_type": "text"
      },
      "source": [
        "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FztgAKuSRj7W",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# To support both python 2 and python 3\n",
        "from __future__ import division, print_function, unicode_literals\n",
        "\n",
        "# Common imports\n",
        "import numpy as np\n",
        "import os\n",
        "\n",
        "# to make this notebook's output stable across runs\n",
        "np.random.seed(42)\n",
        "\n",
        "# To plot pretty figures\n",
        "%matplotlib inline\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "mpl.rc('axes', labelsize=14)\n",
        "mpl.rc('xtick', labelsize=12)\n",
        "mpl.rc('ytick', labelsize=12)\n",
        "\n",
        "# Where to save the figures\n",
        "PROJECT_ROOT_DIR = \".\"\n",
        "CHAPTER_ID = \"svm\"\n",
        "\n",
        "def save_fig(fig_id, tight_layout=True):\n",
        "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
        "    print(\"Saving figure\", fig_id)\n",
        "    if tight_layout:\n",
        "        plt.tight_layout()\n",
        "    plt.savefig(path, format='png', dpi=300)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GfqjdA45Rj7a",
        "colab_type": "text"
      },
      "source": [
        "# Large margin classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GEYBcznhRj7a",
        "colab_type": "text"
      },
      "source": [
        "The next few code cells generate the first figures in chapter 5. The first actual code sample comes after:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DrrkfXnFRj7b",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "2275888d-3500-47d1-93bc-b409bd2af137"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "from sklearn import datasets\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
        "y = iris[\"target\"]\n",
        "\n",
        "setosa_or_versicolor = (y == 0) | (y == 1)\n",
        "X = X[setosa_or_versicolor]\n",
        "y = y[setosa_or_versicolor]\n",
        "\n",
        "# SVM Classifier model\n",
        "svm_clf = SVC(kernel=\"linear\", C=float(\"inf\"))\n",
        "svm_clf.fit(X, y)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=inf, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
              "    decision_function_shape='ovr', degree=3, gamma='scale', kernel='linear',\n",
              "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
              "    tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OKzLEfYTRj7g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        },
        "outputId": "78a5a761-8b5c-41e3-d392-5e2542767eb9"
      },
      "source": [
        "# Bad models\n",
        "x0 = np.linspace(0, 5.5, 200)\n",
        "pred_1 = 5*x0 - 20\n",
        "pred_2 = x0 - 1.8\n",
        "pred_3 = 0.1 * x0 + 0.5\n",
        "\n",
        "def plot_svc_decision_boundary(svm_clf, xmin, xmax):\n",
        "    w = svm_clf.coef_[0]\n",
        "    b = svm_clf.intercept_[0]\n",
        "\n",
        "    # At the decision boundary, w0*x0 + w1*x1 + b = 0\n",
        "    # => x1 = -w0/w1 * x0 - b/w1\n",
        "    x0 = np.linspace(xmin, xmax, 200)\n",
        "    decision_boundary = -w[0]/w[1] * x0 - b/w[1]\n",
        "\n",
        "    margin = 1/w[1]\n",
        "    gutter_up = decision_boundary + margin\n",
        "    gutter_down = decision_boundary - margin\n",
        "\n",
        "    svs = svm_clf.support_vectors_\n",
        "    plt.scatter(svs[:, 0], svs[:, 1], s=180, facecolors='#FFAAAA')\n",
        "    plt.plot(x0, decision_boundary, \"k-\", linewidth=2)\n",
        "    plt.plot(x0, gutter_up, \"k--\", linewidth=2)\n",
        "    plt.plot(x0, gutter_down, \"k--\", linewidth=2)\n",
        "\n",
        "plt.figure(figsize=(12,2.7))\n",
        "\n",
        "plt.subplot(121)\n",
        "plt.plot(x0, pred_1, \"g--\", linewidth=2)\n",
        "plt.plot(x0, pred_2, \"m-\", linewidth=2)\n",
        "plt.plot(x0, pred_3, \"r-\", linewidth=2)\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.legend(loc=\"upper left\", fontsize=14)\n",
        "plt.axis([0, 5.5, 0, 2])\n",
        "\n",
        "plt.subplot(122)\n",
        "plot_svc_decision_boundary(svm_clf, 0, 5.5)\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\")\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\")\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.axis([0, 5.5, 0, 2])\n",
        "\n",
        "# save_fig(\"large_margin_classification_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 864x194.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E9dVXSCwRj7i",
        "colab_type": "text"
      },
      "source": [
        "# Sensitivity to feature scales"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tNXE0KeMRj7j",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "b6272c20-fef7-4bd0-ef03-165d7f681093"
      },
      "source": [
        "Xs = np.array([[1, 50], [5, 20], [3, 80], [5, 60]]).astype(np.float64)\n",
        "ys = np.array([0, 0, 1, 1])\n",
        "svm_clf = SVC(kernel=\"linear\", C=100)\n",
        "svm_clf.fit(Xs, ys)\n",
        "\n",
        "plt.figure(figsize=(12,3.2))\n",
        "plt.subplot(121)\n",
        "plt.plot(Xs[:, 0][ys==1], Xs[:, 1][ys==1], \"bo\")\n",
        "plt.plot(Xs[:, 0][ys==0], Xs[:, 1][ys==0], \"ms\")\n",
        "plot_svc_decision_boundary(svm_clf, 0, 6)\n",
        "plt.xlabel(\"$x_0$\", fontsize=20)\n",
        "plt.ylabel(\"$x_1$  \", fontsize=20, rotation=0)\n",
        "plt.title(\"Unscaled\", fontsize=16)\n",
        "plt.axis([0, 6, 0, 90])\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "scaler = StandardScaler()\n",
        "X_scaled = scaler.fit_transform(Xs)\n",
        "svm_clf.fit(X_scaled, ys)\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.plot(X_scaled[:, 0][ys==1], X_scaled[:, 1][ys==1], \"bo\")\n",
        "plt.plot(X_scaled[:, 0][ys==0], X_scaled[:, 1][ys==0], \"ms\")\n",
        "plot_svc_decision_boundary(svm_clf, -2, 2)\n",
        "plt.xlabel(\"$x_0$\", fontsize=20)\n",
        "plt.title(\"Scaled\", fontsize=16)\n",
        "plt.axis([-2, 2, -2, 2])\n",
        "\n",
        "# save_fig(\"sensitivity_to_feature_scales_plot\")\n"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-2.0, 2.0, -2.0, 2.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Onco//vEPq11Nr9MhhLg0SbyFEEIIFxMQEMDvf/97lixZQm5uLv/+978JDw8nJibGavO3v/2NoUOH8s4773Do0CEnRiuEKCWJtxBCCOHC/Pz8+N3vfsfChQvp2bOntT8hIYFVq1bx2GOP0aZNG4YMGcLf//53MjIynBbr3LkQEmJfHTgkxL4tRH0iibcQQghRBy1cuJC5c+cyceJEGjRoQGpqKk8++STBwcE888wzNR7P3LkwdSqkp4PW9u9Tp0ryLeoXSbyFEEKIOqhJkybceeedxMfHc+TIEb766isMw8DHx4fevXtb7b777jtmz57Nnj17rmo8L7wAFRflzM+37xeivlB14eGLfv366Y0bNzo7DCGE+M2UUpu01v2cHUdNkj7bufLz83Fzc6NBgwYAPPDAA3z88ccA9OnTB8MwMAyDzp07X9H3dXOzj3RXpJR9oTIhXEF1+2wZ8RZCCCHqER8fHyvpBoiJieGuu+6iSZMmpKWlMWPGDLp06ULPnj15//33r9j7Bgf/tv1C1EWSeAshhBD12JgxY5gzZw6HDx9mwYIF3HfffTRr1oytW7dy8OBBq92RI0f48ccfL7tM4WuvgY9P+X0+Pvb9QtQXkngLIYQQAm9vb2s1zNzcXBYvXswDDzxgHZ87dy69e/emc+fOPP/882zevPk3JeGTJ8OHH0L79vbpJe3b27cnT74an0aI2kkSbyGEEEKU4+XlxZgxY+jQoYO1z2azERAQwO7du3njjTcIDQ3l2muv5emnn6aqc/YnT4YDB+xzug8ckKRb1D+SeAshhBDikv7whz+QnZ3NihUreOSRR2jZsiX79+/nrbfeYubMmVY7m82GTZ6WFMIhSbyFEELUqOzsbHbt2uXsMMRlcHd3t1bDzMzM5Ntvv2XatGlMmTLFarN8+XKCg4N5/PHHWb16NcXFxU6MWIjaRcoJCiGEE9XHcoJKKQ3Qs2dPq3Rdt27dnB2WuEKefvpp3nrrLWu7ZcuWTJo0CcMwuOmmm/Dw8HBidEJUT3X7bEm8hRDCiVw58VZKPQrcB/QE/qu1vq8qr/P399dFRUWcOnXK2te1a1crCe/ZsydKqasRsqgBWms2btyIaZrExsayf/9+69jAgQNZu3atE6MTonqkjrcQQghnOQS8Cvz7t7woJCSEw4cPk5KSwpQpU2jRogXbt29n1qxZ9O7dmy5duvDCCy+wZcuWyy5dJ5xHKUX//v2ZPXs2e/fuZdOmTTz33HNcd9113HzzzVa7rKws7r//fhYtWsT58+edGLEQNUdGvIUQwolcecS7lFLqVaBtVUe8K/bZhYWFrFy5EtM0iY+P5+jRo9axDh06WCPh/fr1k5FwF6a15vz583h7ewPwzjvv8NhjjwHQtGlToqKiiImJYdSoUVYbIWobmWqCJN5CCNdVXxJvpdRUYCpAcHBwaHp6usN2RUVFfPvtt1YSnpubax0LDg62kvCBAwfi5iY3bV3Znj17+OKLL4iNjWXr1q3W/iZNmhAdHc3HH38sF1qi1pHEG0m8hRCuq74k3mVVtc8uLi4mNTUV0zSJi4vj0KFD1rE2bdoQHR1NTEwMgwcPliTcxe3YsYO4uDhM0yQtLY3w8HAWLlwI2P8dJCUlMWbMGHx9fZ0cqajvJPFGEm8hhOuSxLtqbDYba9euxTRNTNMkIyPDOtaqVatyVTPc3d1/07lF7bJnzx7y8/Pp1asXACtXrmTYsGE0bNiQ8PBwYmJiiIiIoFGjRk6OVNRH8nClEEKIOs/NzY3Bgwfz17/+lfT0dNatW8f06dMJCQkhOzubd999l2HDhtG6dWseeughli1bRlFRkbPDFpfhuuuus5JusI94Dxo0iLNnzxIXF8ftt99OQEAAEydOZO7cufL3LFyKjHgLIYQTufKIt1LKA/AAXgLaAr8HirTWF82ErmSfrbVm8+bNVum6vXv3Wsf8/PyYMGEChmEwYsQIPD09r8h7CufIyMiwpqOkpqYC9nn/Bw4csOaCnz59WkbCxVUlU02QxFsI4bpcPPF+GXvSXdYrWuuXL/a6q9Vna6358ccfrSR8586d1rHmzZsTFRWFYRiMHDlSqma4uKysLBISEvDw8OChhx4CIDc3l/bt2zNs2DAMw2DChAn4+fk5OVJR10jijSTeQgjX5cqJ9+WqiT5ba83PP/9MbGwspmmybds261iTJk0YP348hmEwZswYGjRocFVjETUjKSmJSZMmYbPZAPvy9sOHD7eS8MDAQCdHKOoCSbyRxFsI4bok8a4Z27dvt6Yp/PDDD9b+Ro0aERkZiWEYjBs3Dh8fnxqNS1xZR44cISkpidjYWL755huKi4sB8Pb25siRIzRu3NjJEQpXJ4k3kngLUS8UFUFGBhw6BOfPg5cXtG4N7dqBh4ezo7tsknjXvN27d1tJ+KZNm6z9Pj4+REREYBgG4eHhMlfYxR07dozk5GRM00QpxYIFCwB7hZzo6GiGDRvGpEmTaNu2rZMjFa5EEm8gNDRUb9iwQeq4ClEXaQ1bt8Lu3fbtkhEsAErLxnXsCD16gAsutiGJt3Pt37/fKlG4fv16a3+DBg0YN24chmEQGRlJkyZNnBilqC6bzWblCGvWrOGmm26yjg0ePBjDMIiOjiY4ONhZIQoXIYk3oJTSJd/x8PCwvpo3b07Z1dGGDRtGVlZWuTbu7u54eHhw99138/DDDwOQlpbGjBkzyrUr+/X6669bc8XmzJnD1q1bHba75pprMAwDgPPnzzN37txy71n2q2/fvrRq1QqwPzSSmZnp8Jyenp7lOoa8vDzc3Nysc7q7u8tKX6Lu0BpSU+Hw4fIJd0Xu7hAYCDfe6HLJtyTetUd6ejrx8fGYpsl3331n7ffy8mLMmDEYhsH48eNp1qyZE6MU1ZWXl8eCBQswTZOUlBTOnTtnHRswYADJyckEBQU5MUJRm7lk4q2Uuh37k/DBQA5wn9Z6tVJqBPBuyf51Jfsdrytc/nwOP0SLFi04duyYtR0SEkJlyxQ/99xzvP766wAsXbqUMWPGVPp++/fvJyQkBIDo6Gji4+Mdths1ahRLly4F4Pjx4xd9ujo2NtZK0t98802ee+45h+2aN2/O8ePHre1rrrmGAwcOlGvj7u6Ou7s7Tz/9NLNmzQJg1apV3HnnnZVeTCQnJ9OmTRsAZs6cyZo1axy269WrF88++ywAZ86c4bnnnrvgQqJ0Ozo6mq5duwKwefNm1q9f7/CcDRs2JCIiwop/7dq1FBYWOjxnQEAAAQEBABQUFHDq1CmH55S7H3XETz/ZR7ovlnSXcne3j3z37Hn147qCJPGunbKysqwkfPXq1ZT+rvT09GTUqFEYhkFUVBQtWrRwcqSiOk6fPk1KSgqmabJw4UKaNWtGRkaG9Ttk7ty5DBgwgI4dOzo5UlFbVLfPrvGJkUqpUcBs4DZgPdCqZL8/EA88AMwHZgFfAYMudc7Q0FA2btyIzWajqKjI+iqu8Mt61apVFBQUlGtT+tW6dWurXZ8+fUhOTrbOUbGtv7+/1fbuu+9mwIABDs953XXXWe08PT257777LmhTev7S0W6Ali1bVnrOirc7fXx88PX1LXe+0q+yF1X5+fnllluuqOzPKi0tja+//tphu+PHj1uJd35+Pv/4xz8qPWe3bt2sxHvRokXMmDHDYTs/Pz+OHj1qbd92220cPHjQYduyF0grV65k7NixDtsppdi3b591gXTvvfeSkpLiMEkPCwvjgw8+AODkyZNERkZekPCXfj311FMMGmT/J5mSkkJSUpLDczZu3Nj6OQF89NFH5OfnX9DO3d2dnj17WotFHDlyhE2bNlV6gdStWze8vLystgUFBZW29XDhec+AfU53haR77up2vPDfnhw85kOwXz6v3fETk28qWcGwuNjevmtXl57zLWqHNm3a8Nhjj/HYY4+Rk5NDQkICsbGxrFq1ipSUFKs/KVs1o3RQQLiORo0aceutt3LrrbeSn5/P7t27raT7yJEj3HvvvRQXF9OrVy9iYmIwDIMuXbo4OWrhymp8xFsp9R3wsdb64wr7p2If4R5csu0LHAX6aq13XOycrjB6UlO01lYy7+bmZiVp586d4+jRo5VeTPTs2dNq+8MPP5Cbm+sw8Q8KCmLEiBGAPfH+6KOPKj3n5MmT6datG2BPUksvZip++fr68tlnn1mfISYmhpycHIdtH3zwQZ544gkAli1bxh133OHwvbXWZGRkWA/NREVFkZyc7PBnFh4ezsKFCwF7HdiWLVtW+vNNSEhgwoQJAMyaNYs//elPDtsFBARw+PBha7tdu3ZkZmY6bDtjxgzrzkRKSkq50f+KDh48SLt27QCYOHEiiYmJDtuNHTuWRYsWAfZfHiEhIZVeTLz//vuMHj0asF8gfPDBBw6TeD8/Pz7//HPrPZ544gmHdxzc3d0ZNWqUdddo7969xMbGOpxi5eHhQUxMjPUQ27p16zh8+LD9PEeO4LF/Px6Ah7s7qTuu4+VYg/zzHkARsI8GnvDm5J+JGZSLu5sbHl5eePTpg2/37i5z4SEj3q7l8OHDJCYmYpomy5cvtwYt3NzcGDp0KIZhMHHixIv2I8I1HDhwgBdffJHk5GR++eUXa3/37t0xDINHH3203ECcqB9casRbKeUO9AOSlVJ7gAZAIvAU0B2wajxprc8opfaW7L9o4i1+VXaee1kNGjSo8pPbvXv3rlI7Hx8fpk2bVqW24eHhhIeHV6ltbGxsldqNHDmSI0eOODxms9nKzXX//PPPOXfunMNkvmHDhla75s2bs3r16krvTPTv37/cZwoMDHR4zop1gadMmcKJEyccti27NLKfnx+jR4++4H1Lv8ou+tGiRQvatGnj8JylF1EARUVF5OfnV/pzLCgosP6cmZlJZQlRxURi3rx5ZGdnO2zr6+trJd47duyodOoUwOjRo63E+7XXXmP+/PkO2zX0HMPZwttLto4CnTlXCE98av8qKzExkaioKMA+dWrmzJkOk/6WLVuSlpZmvW7EiBEcO3bM4UXCPffcw7333gvYp07Nnj270ouJmTNnWvOAv/jiC3bv3l3pcyDCtQQGBjJ16lSmTp3KsWPHSEpKwjRNli1bxvLly1m+fDmPPPIIYWFhGIbBpEmTyt1RFa4jJCSEOXPmUFBQwLJlyzBNk8TERLZt28b27dt55JFHrLY5OTkEBQXJM1bikmp6SCgI8AQM4CagEEgCZgCNgIpZ1CnAYdHNkhHyqYA8hSwuUHGOd+PGjatUv9XLy4shQ4ZU6T1CQ0MJDQ2tUttXXnmlSu0GDhzIkiVLqtT2448/vnQj7Anz6dOnHSboxcXF5R4imjp1KhEREQ7bVryY+7//+79Kz3vDDTdY7Tp06MAzzzxT6cWEr6+v1XbAgAGA/WKh6PBhis6do8hmo6i4mO93da/wyTpiH/kuolXz0xQVF1NUXEwxlLtAKTsFq+xFBtifhyhr27Zt5ObmOvw5hoWFWX/OzMxk3rx5lf3Ief75560/f/HFF9YdlYoiIyMrPYeo/fz8/JgyZYp1YT1//nxM02TJkiWsWrWKVatW8dhjj3HjjTdaVTNK71gJ1+Ht7U1ERAQRERF88MEHrFixgp9++smaWmSz2ejfvz/e3t4YhoFhGISGhkoSLhyq0akmSqnmwHHsU0o+K9kXjT3x/hbw1Fo/XKb9T8DLWuu4i53XlW9bCiEqkZpqr9ldIuThcNKP+l7QrL3/GQ68l/Lrjtat7dVNSthsNivxdjQlqezzFdu3by/3HEjZ14SEhHDttdcC9gfv1qxZU+nFxAMPPGAtxPLFF1+wc+dOhxcoPXr04OGHH5apJnXML7/8YiXhixYtKnfBN3DgQCsJlzsedcOBAwcYMGBAuTuwISEhVhI+YMAAScLrEJeraqKUygBe0Fr/p2R7EvAi8E/gXq31jSX7fbGPgF8vc7yFqIf274ctW6yHK+eubsfUD/qVzPG28/Eq4sMHN/76gKW7O/TtCy6U0Mgc77otLy+vXNWMs2fPWsdCQ0Ot5Kzsw/jC9RQXF7N69WpM0yQuLo6cnBzr2Jo1a7ixzGCAcG2umHjPBMYBEdinmiQDK4G3gT3AFGAh8Apws9b6klVN6lMnLkS9UVQEyclVr8OVPEMAACAASURBVGoC9sR7/HiXqmoiiXf9cebMGRYvXoxpmsyfP58zZ85Yx/r06WMl4Z07d3ZilKK6bDYb3333HaZpkpqaytq1a61pbffddx+NGzfGMAyGDBlywXQ3Ufu5YuLtCfwfcCdwDpgHPK21PqeUGgm8A7Tn1zreBy51zvraiQtR50kd7zpJ+mw4e/YsS5cuJTY2luTkZPLy8qxjPXr0sJLwbt26yTSFOuL48eMEBQVRVFQEQFBQEJMmTcIwDMLCwlymElN953KJ99UgnbgQdZSsXFknSZ9dXkFBAV9//TWmaZKUlMTJkyetY126dLGS8F69ekkS7sK01mzcuBHTNDFNk3379lnH/P39iY2NZejQoc4LUFSJJN6Aj4+P7tat20UXEqlsqfba3E46WCGwJ99bt9pHvqF8Au7hYT/esSP06OFySTdI4i3KO3/+PMuXL8c0TRISEsqtVNyxY0crCe/bt6/8jnBhWmvS0tIwTZPY2Fj27NnDoUOHrLKt8+bNo1GjRowcObJceVjhfJJ4U/mS8a7Ozc2tWol8bbqIuNx2bm5u8stF2BUVQUaGvdJJYSF4etormLRr51JzuiuSxFtUprCwkFWrVmGaJvHx8eWqZlxzzTVWEt6/f3/pJ12Y1pp9+/ZZVZO01oSEhHDw4EGaNm3K+PHjiYmJYdSoUResEXFRZfvM8+fBy6tO9JnOJok30K1bN/2f//zHYbmuyhZCcYV2ws6ZFwa15aKkYl1yUXdI4i2qoqioyKqaER8fX65qRnBwMNHR0RiGwaBBg6S/cHHnzp3jrbfewjRNfvzxR2t/48aNueWWW5g+fTp9+/at/AQXu0tY+jCnC98ldDZJvKmbnbjWGpvNVu1EvrZcRFxuO5vN5uy/ilqh7IqkteXCoKbf293dvU6O6kniLX6r4uJiq2pGXFwcWVlZ1rE2bdpYSfjgwYOlaoaL27VrlzUnfMuWLQB88803DB8+HID09HT8/f1/XYisHjwX42ySeCOdeF1WuviJMy8MnH1RUlhY6Oy/hlqjNDGvDXchrtTFy/XXXy+Jt7hsNpuNdevWERsbi2maZGT8Wl6zZcuWVtWMm266CQ8PmV7gyvbu3UtSUhLTpk2z/i4jIiJYsWIF4eHhGIZBREgIjQ8dqtOVoJxNEm+kExd138XuftSXi5LiqvwicU2SeIsrQmvNhg0brBHS/fv3W8cCAgKYOHEihmEwdOhQPD09nRipuBJsNhvDhw9n1apV1j5vT0/G9u6NMWgQt/Trx4JNnevc2gfOVmOJt1JqKTAKMMou4a7s934/Ae4FZmutn73cYC6XS3fiRfLwgxBVobUul5TXxqlRl9MuLS1NEm9xxWmt2bJlS7mqGaX8/PyYMGEChmEwfPhwqZrh4jIzM4mLi8P8/HNSN22iNK+7O+xJ4tb+b51b7dfZajLx7g1sBnYCPbXWxSX7/wL8AfhQa/3g5QZSHS7ZicvDD0IIZI63uPq01vz0009WEr5jxw7rWLNmzYiKisIwDEaNGoW3t7cTIxXVkprKoa1bSVi/HnPdOnYfSiDrRMeSgy8CG4AY2rYYScb76399XevW9rneokpqdKqJUupT7CPbv9Naf6qUeh54Dfvqk3dorZ3yJJzLdeLy8IMQooQk3qKmbdu2zZqOsnXrVmt/kyZNuOWWWzAMgzFjxtCwYUMnRil+sxUr4OhRa9PtNgOtS3OHzsCukj+7M7JnN4xBg5jQvz9BHTuCLNxTZTWdeLfD/jeXA/wF+AewBBivtT5/uUFUl8t14vVgGWwhRNVI4i2caceOHfZpCqZJWlqatd/X15fIyEhiYmIYN24cPj4+ToxSVElqqn3aaomQh8NJP1pS7YSjQBIQC3wD2EsWuynF7P/5H6a/+24NB+u6avzhSqXUG0DpPO7vgFFa6/wKbcKA6UAo0JqSEfLLDfJSXKoTLyqC5GQr6U79vR+Fpy6suerZ1MaN/zpm35CHH4SosyTxFrXFnj17rCS87N+Pj4/Pr1UzIiJo1KiRE6MUldq/H7ZssfKLuavbMfWDfhfM8f7rvd/g7ZmMuXYtS3/8kYUff8yoe+4BYOnSpWzfvp3o6Gjatm3rlI9R2zkj8f4D9tFugK5a6x0O2oQDQ7DPCf8P8PDVTLwDAgJ0TEzMBWW6fH19eeGFF6x2//73v8nLy3NY9qt79+5WQfqjR4+ycePGSst/de3a1ZoHd/jwYQoKCipte8GT4xX+Y6y8NaDSzzV0XskqZfLwgxB1liTeojbav3+/lYSvW7fO2t+gQQPGjh2LYRhERkbStGlTJ0YpyqkwsAf25PtiVU1OnjtHo5gYPEpWxIyKiiI5ORmAG264AcMwiI6Opn379jX7WWqxmp5qcifwOZALtATe11r/zyVecxp49Gom3pUtGd+sWTNOnDhhbXfo0KFceaWynnnmGd58800Avv76a0aPHl3p++3du5cOHToAEBMTg2maDtuNGDGCZcuWAXDy5Elat26Nh1K4K4WHmxse7u4Un/TEHXce53EGMQiAxSwmkUSad7Th4e5u/2rYEA9/f5o2bcqXX35pvccf/vAHjh8/7vBiYsSIEYSHhwP2TvTLL7+stNawYRg0adIEgPXr15OTk+PwQqJ58+Z07doVsC/isGfPnkprF/v6+krJKiEuQRJvUdsdPHiQ+Ph4TNMkNTXV2u/l5cXo0aMxDIPx48fTvHlzJ0YpgGpPZY2Li+O///0vKSkpnD171trfv39/nnzySe64446rEbVLqW6fXeW5CyWj2J8CW4ERwGrgAaXU37XWOy83gCshODiYZ5555oIyXRWTvt/97nccPXrUYUmvPn36WO2aN2/O6NGjKy0J1qDkyhCgRYsWtG3b1uE5yz4dXlRUVO4fcUXn+XWK/FGOspOdsPvCdn5+fuW24+LiOHjwoMNzNmjQwEq8d+3axfPPP1/p+w8fPtxKvGfPnk18fLzDdqNGjWLp0qWA/WKiS5culZ7TNE2io6MBeOONN3jxxRcdJun+/v5s27bNet3o0aPJzc11eJEwefJk7r//fgB++OEHXn311UrvNrz88svWz+vLL79k586dDtu1b9+eyMhIAAoKCkhISKj0YqJHjx4EBNjvUuTm5l4QZ9k7HaXtAAoLC3F3d5elnIUQLic4OJgnnniCJ554gqysLBISEjBNk2+//ZYFCxawYMECPD09GTlyJIZhEBUVdcHvKlFDevSAU6eqXryhR49yu6Ojo4mOjub06dMsWrQI0zRZsGABGzZsICcnx2qXlZXFmTNn6NSp09X6JHVWlRJvpdQQwAQygTFa6yNKqRnYZ+nPBiZcvRAvLSAggIcffviS7V588cUqna9fv34sWbKkSm0/+OCDKrXz8/PjzJkzFK1ZQ1FWFkXFxRQVF7PmoeYUU0wzmlltxzGOfvSj96vHrHZFzZtT1LnzBYnbX//6V/Ly8hwm/gMHDrTahYSE8Oyzz1Z6MdG4ceNyn7+wsNDhObt161bu/Tt16lRp/eKKFx7FxcUUFxdTUFBQ7hwV77ps376dzMxMhz/HwYMHW38+dOhQpXcbAJ5++ulyiXdSUpLDdmPHjrUS71OnTl30ij4uLo5JkyYB8NFHHzFjxgyH7fz9/Tly5Ii1fe2115KRkXHB0u/u7u5Mnz7dmhK1atUq7r///kovJkzTpGXLlgC8/vrrrFu3zmG7Xr168fjjjwNw+vRpZs2aVenFxPjx47nuuusA+8VMWlqaw3M2bNjQWqYYYMuWLRQXFztctbF58+Y0a2b/N11YWEhBQUG5962LS7+Lqjt16hTnzp0rN4ghXEObNm149NFHefTRR8nJySExMZHY2FhWrlzJokWLWLRoEVOnTmX48OEYhsGECRMIDAx0dtj1h1L2SmiVlSv28LBXVrtEueJGjRoRExNDTEwM+fn5LFmypFxO8d577/H666/Tq1cvDMPAMAzrbri4uEtONVFK9QFWAmeBIVrrvWWObQD6AWFa69WVvP6qTzVxqduW9XSOd8XFT8om6TabjVatWlltd+7cyblz5xwm/u3bt7eSxOzsbFavXl3pgiW/+93vrIeAvvzyS7Zv3+7wAqFr16488sgjgH0U/6GHHqr0YmLWrFkMGTIEsF90vfvuuw7jbNGiRbkyXe3bt6/0zsSf/vQnXnnlFQAWLFjALbfcUunPMTMzkzZt2gDl5+JVFB4ezsKFCwHIyckp9/OtKDExkaioKABmzpzJSy+95LBdUFBQuRGPtm3bkpWV5bDtjBkzmDVrFgApKSlERESUO+7m5mYl4Tt37rQe4pkyZQrLli1zmPiHhYXx97//HYATJ05w2223OVya3d3dnSeffJLQ0FAAFi9ezOLFix2es0mTJkybNs2Ka86cOZw7d87hObt27Wr9Yjl27Bjbtm1z2M7Dw4MOHTpYd9xOnjzp8ALFzc0NpVS9nGqilNKNGze2SteNHTtWSte5uCNHjpCYmIhpmnzzzTfWSrNubm7cfPPNGIbBpEmTrIEDUQPKLtBXWAienldsgb4ZM2bwzjvvcOrUKWtft27dMAyDW2+9le7du1c3+lrrqs7xVkpdB6wBvIGbtdY/Vjg+EvgaWKe1HlTJOSTxLkuqmtRrjpZ+9/b2xtfXXvLpzJkzHDp0qNKLif79+1t3EtavX092drbDxL9NmzaMHTsWgLy8PN57771KV1ecMmUKPUpuNyYmJpKQkOCwbdOmTfniiy+szxIREUFubq7DttOmTeMPf/gDYE+8b7311nLvWdahQ4esC4PIyEjrgqGiW265xbrQOHTokHUB4khycrJ1AfPSSy8xc+ZMh+1atmxJdna2td26dety22W99NJLvPzyy8ClL5CysrJo3bq1FfeCBQsq/Uzz58+vd4m3j4+PLjv1ztfXl4iICAzDYOLEiXhIX+fSjh07RnJyMqZp8vXXX1NYWAiAUoqbbrrJSsIv9n9Y1H7nz59n2bJlmKZJYmKi9UzdlClT+PjjjwH7s2Clgwx1RY1XNfnNbyCJ94Wkjreox7TW5S5AGjZsaE2hOnr0KPn5+Q6T+caNG9Oxo30VtnPnzpW721HxYmLo0KHWKPr333/P2rVrHd5x8fHxKffsw9NPP82JEyccnvf222/ntttuA2DNmjU899xzld7FSU1Nxd/fH4A777yTJUuWXNDOZrMxfvx4kpOT613i3a9fP/3VV19ZVTM2bNgAQKtWrcjMzLT+Pch0FNd38uRJ5s+fj2maLF68mPPnf32eafDgwVbVjODgYCdGKaqrsLCQFStWYJomt99+uzUt8b///S8vvviiNR0lNDTU5ZPwWpl4K6UaAdeVbH4HvAkkA8e11o7vt1eDyyXesnKlEPWezWbDZrPh6elZLxPvsn12eno6cXFxuLu7W88mHD16lJCQEEaMGIFhGNxyyy3WcwPCNf3yyy8sWLAA0zRZtGgR586ds44NGDDASs6uceFplaK8++67j88++8zabt++vfX3PGDAAJcsOFBbE++hwAoHhz7TWt93pd/P5RJvsCff1Xz4QQjh+lx9jrdSqgXwMTAa+/J4z2mtv7jYa6rSZycnJzNhwgTr4WtPT89ypetatGhxZT6AcIrTp0+TkpKCaZosXLiQ/Pxf1+ELDQ21RsJL73IJ11R6B9A0TeLi4jhUZmXNstMHXUmtTLxrmksm3qWu4sMPQojarw4k3v8F3ID7gT7AQmCw1npbZa+pap+dnZ1t1Y/+9ttvsdlsAHh7e5ObmyuLt9QR+fn5LF68mNjYWBYsWMDp06etY71797ZGSC9WvlbUfjabje+//x7TNDFNk2nTpvHUU08B8PPPP/PPf/4TwzAYMmQI7u7uTo62cpJ44+KJtxCiXnPlxFsp5QucAHporXeV7JsDZGmtn63sdZfTZ+fm5lpVM8C+0BnYf5lPnjyZm2++mYkTJxIUFFT1k5Yd+Dh/Hry8ZODDyc6ePcvSpUsxTZPk5GR++eUX61j37t2tJLx79+4uP1e4PrPZbBQWFlrFAso+BB8YGMikSZMwDIObb7651j1sLYk3kngLIVyXiyfefYFUrbVPmX3TsVfBqrTsS3X77OLiYmtEbN26dQwaZC+q5ebmRlhYmFU1o9Iymheb6lc60iZT/ZyuoKCgXNWMkydPWse6dOliJeG9evWSJNzF/fTTT3zxxRfExsayd69VtRo/Pz/uu+8+/vznPzsxuvKq22e73qx2IYQQtUUj4JcK+04BjSs2VEpNVUptVEptLLu41OUoexu6S5cufPLJJ0RERODu7s7KlSt59NFHadOmDTfddNOF5SFLH24vrSxV8QH30n27d9vb1YHBKVfl7e1NREQEn3zyCbm5uSxevJgHHngAPz8/duzYwauvvkqfPn3o1KkTzz33HJs2bbpgQTbhGnr27Mkbb7zB7t272bJlCy+88AKdOnXi2LFj5RajO3PmDCkpKeWq47gaGfEWQggnqoMj3n8Ehl7NEe/KnDp1qlzpuqZNm3Lo0CErUTdNk36NGhGSny/lXF1YUVERK1euxDRN4uPjyyVmISEh5apmyEi469Jas23bNmsBM4DY2FhuvfVWmjZtyvjx4zEMg9GjR9do2VGZaoIk3kII1+XiiXfpHO/uWuvdJfv+Axy60nO8f6u8vDx27txJv372H+2JEycIDAykqKiIftdeS8ygQYQkjSXwdNsLXisLmLmO4uJiVq9ebVXNKLu6brt27YiOjiYmJoZBgwa5ZOk6UV58fDyvvPIKP/7463qOjRo1slbBnThx4lW/2JLEG0m8hRCuy5UTbwCl1JeABh7AXtUkhStU1eRKOnDgAM88+igLv/mGM2XqR3ekI2GEcQu30JRfq6QMnVcyiuruDn37gtSWrvWKi4vLVc3IysqyjrVu3Zro6GgMw+DGG2+s1VUzxKXt2rXLWoBr8+bNAFx//fVs2rTJapOfn4+Pj09lp7hskngjibcQwnXVgcS7BfBvYBRwDHj2StTxvipSU8nfv58lP/yAuXYtiWs2k08+CsU85uGPfbXRU5wial6ZOaStW9sXMhMuw2azsX79emJjYzFNk4MHf127LygoyKqaERYWVuuqZojfZt++fcTFxdGyZUvuvvtuwF6esF+/fowbNw7DMIiMjKRx4wsePbkskngjibcQwnW5euJ9OZzWZ69YAUePWptLb23KRjayl73cjf0XtkZzJ3fSvI07xqBBxNxwAz2uvx41bFjNxyuuCK01GzdutEbC9+3bZx3z9/dn4sSJGIbBsGHD8PT0dGKk4kr56KOP+P3vf29te3t7M2bMmCuyCq7LJt5KqY7AT4Cptb6rZN+dwBuAP/A1MEVrffxS55LEWwjhqiTxrkGpqfaa3SVW3hpwQZNccvk9vyePPGtfp3btMO6+G8Mw6NOnjzyw58K01qSlpWGaJrGxsewuLSkJtGjRggkTJmAYBiNGjMDLy8uJkYrqyszMtBbgWrNmjVXxxs/Pj5ycnMu+0+HKifdSoCGQrrW+SynVHVgLRACbgQ8BN6317Zc6lyTeQghXJYl3Ddq/H7ZssSqaOEq8AYoowvbCSsy1a0nYsIGjZRZxWblyJTfffHONhCuuLq01W7dutZLw7du3W8eaNm1KVFQUhmEwatSoGq2aIa687OxsEhISME2Ttm3b8p///AewzwO//fbbGT9+PBMmTMDf3/+S53LJxFspdTswCfgZuK4k8X4dCNFa31nS5lpgO+Cntc6r/GySeAshXJck3jWoqAiSk63EO/X3fhSeurDSRdmqJkXAt82aYSYk8O2335KWlmaNlD300EP4+vpiGAYDBw6Uqhku7ueff7amo/z000/W/saNG1tVM8aOHUvDhg2dGKWoLpvNZv1fjY+PJzo6GrCvDzB06FCrOkplq+C6XOKtlGoCbASGY38KvjTxTgK+01rPLtP2NPYV0DY5OM9UYCpAcHBwaHp6eo3EL4QQV5Ik3jXsp59+XTznUirU8dZaW9NMTp06RWBgoLWQR5s2bayqGYMHD5aqGS5u586dVtWMLVu2WPt9fX2JjIzEMAzGjRuHr6+vE6MU1XX8+HFrJHzZsmUUFRUB9lVwb7rpJhYuXHjB37Errlw5C/hYa51ZYX8j7CueleVwBTQArfWHWut+Wut+AQGObxcKIYQQ5fToAYGBvy4NXxl3d3u7Hj2sXWXndjdu3Jjly5fzxBNP0LZtW7Kysnj77bcJCwujbdu2rFix4mp9AlEDOnfuzPPPP8/mzZvZs2cPb775Jv369ePMmTN89dVXxMTEEBAQgGEYfPnll+TlXfTGvKilWrRowf3338+iRYs4fPgwn376KZGRkXh4eHDixIlySfdnn31GRkZGtd+zRke8lVJ9gLlAX631eaXUy5Qf8U7VWv9vmfZ52FdAu2DEuyyZaiKEcFUy4u0EWsPWrfaRbyg/+u3hYT/esaM96a7Cg5Q2m40NGzZY0xQOHDjAwYMHadeuHQCJiYk0atSIoUOHSuk6F3fgwAFrJHzt2rXWfm9vb8aOHWtVzWjatOlFziJqu1OnTpGRkUGPkgvvXbt20blz59LDrjPVRCn1BPAaWI+LNwLcsc/lXgy011pPLmnbAdiBzPEWQtRhkng7UVERZGTYK50UFoKnp71md7t2l71Spdaa7du3061bN2u7U6dO7NmzBz8/P6t03fDhw6V0nYvLyMiwqmakpqZaVTO8vLwYPXo0hmEwfvx4mjdv7uRIRXVt27aNl156ieXLl3PixAmXSrx9gCZldk0HQoD/AQKB7/m1qskHgIdUNRFC1GWSeNdtBQUFzJo1i9jYWHbt2mXtb968OVFRUTz++OP06dPHiRGKK+HQoUPWXOFvv/0Wm80GgIeHByNHjsQwDKKioqpUNUPUXoWFhXh5eblO4n3Bm5eZalKyfSfwJuAHLAN+J3W8hRB1mSTe9YPWmm3btlnTUbZt2wbA4sWLGTNmDABZWVn4+flJ6ToXl5ubayXhK1assJJwd3d3hg0bZlXNCAwMdHKk4nK4XFWTq6E+duJCiLpBEu/6afv27SQmJjJ9+nRrysnEiRNZtmwZkZGRxMTEMHbsWHx8fJwcqaiOI0eOkJSUhGmafPPNN+WqZoSFhRETE8PEiRNp1aqVkyMVVSWJN9KJCyFclyTeAuwPaIaFhZGammrt8/HxISIiAsMwCA8Pp1GjRk6MUFTX8ePHSU5OxjRNli5dSmFhIWCvljNkyBAMw2DSpEm0bdvWyZGKi5HEG+nEhRCuSxJvUda+ffusqhnr16+39v/5z3/mj3/8oxMjE1fSyZMnmT9/PqZpsmTJEgoKCqxjN9xwA4ZhEB0dTfv27Z0YpXBEEm+kExdCuC5JvEVl0tPTiY+PJzY2li+++IKQkBAAXn31VdavX29VzWjWrJlzAxXV8ssvv7Bw4UJM0yQlJYVz585Zx/r3749hGBiGQYcOHZwYpSgliTfSiQshXJck3uK36t69Oz///DMAnp6ejBo1yqqa0aJFCydHJ6rj9OnTLFq0CNM0WbBgAfn5+dax66+/3krCO3bs6MQo6zdJvJFOXAjhuiTxFr9VTk4OCQkJxMbGsmrVqnKl69544w2mT5/u5AjFlZCfn8+SJUuIjY1l/vz5nD592jrWq1cvKwnv2rWrE6OsfyTxRjpxIYTrksRbVMfhw4dJTEzENE2WL19OUlISERERAKxcuZIdO3YwceJEgoKCnBypqI5z586xdOlSTNMkKSmJX375xTrWrVs3Kwnv0aMHqgqrrYrLJ4k30okLIVyXJN7iSjl27BiNGzfGy8sLAMMwiIuLQylFWFiYVTWjdevWTo5UVEdBQQHffPMNpmmSmJjIiRMnrGOdO3e2kvDevXtLEn4VSOKNdOJCCNclibe4Wr766is+//xzli5dyvnz5639N954I4899hi33XabE6MTV0JhYSErVqzANE0SEhI4evSodezaa6+1kvDQ0FBJwq+Q6vbZblcyGCGEEELUDrfddhvz58/n8OHDfP7550yYMAFvb29SU1M5cOCA1S43N7fctnAdnp6ejB49mg8//JDs7GyWLVvGQw89RGBgIHv37mX27Nn079+fa665hunTp7N27VrrmQDhHDLiLYQQTiQj3qIm5eXlkZKSwuDBg2nXrh0Ar7zyCi+//DL9+vWz6kdfd911To5UVEdxcTFr1qzBNE3i4uLIzs62jrVt25bo6GhiYmK44YYbcHOTMdjfQqaaIJ24EMJ1SeItnO3555/n7bff5syZM9a+Pn36YBgGMTExdOrUyYnRieqy2Wx8//33xMbGEhcXR2ZmpnWsVatWREdHYxgGQ4YMwd3d3YmRugZJvJFOXAjhuiTxFrXB2bNnWbJkCaZpkpycTF5eHgB33XUXc+bMAUBrLfOEXZzNZmP9+vWYpolpmqSnp1vHAgMDmTRpEoZhcPPNN+Ph4eHESGsvSbyRTlwI4bok8Ra1TUFBAV9//TWmaXLHHXcwZswYAOLi4njxxRetB/Z69uwpibgL01qzadMmTNMkNjaWffv2Wcf8/f2ZOHEihmEwbNgwPD09nRhp7SKJN9KJCyFclyTewlVMmTKFTz75xNru2LGjlYT37dtXknAXprXmhx9+sJLwXbt2WceaN2/OhAkTMAyDkSNHWuUq6ytJvJFOXAjhuiTxFq6isLCQVatWERsbS0JCAkeOHLGOjR8/nqSkJCdGJ64UrTVbt261pqP8/PPP1rGmTZsyfvx4DMNg9OjRNGjQwImROoeUExRCCCHEVefp6cnIkSP54IMPOHToEMuXL+fhhx8mKCiIgQMHWu12797NH//4R77//nspXeeClFL07NmTV155hW3btrFt2zZmzpxJr169OHXqFHPmzCEqKoqAgADuvPNOEhISOHv2rLPDdhky4i2EEE4kI97C1RUXF1NQUICPjw8Ar732GjNmzACgTZs2VtWMwYMHS9UMF7dr1y7idLl7NwAAG1VJREFU4uIwTZPNmzdb+319fYmIiMAwDMLDw/H19XVilFeXTDVBOnEhhOuSxFvUNWlpacyZMwfTNDl48KC1v2XLltxzzz3Mnj3bidGJK2Xfvn3WdJQNGzZY+xs2bMi4ceMwDIPIyEgaN27sxCivPJlqIoQQQohao0+fPvzlL3/hwIEDrFu3jqeeeoqQkBBycnLIyMiw2p09e5Zly5ZRVFTkxGjF5erQoQNPP/0069ev58CBA/zlL3/hhhtu4OzZs8THx3PnnXcSEBBAVFQUc+bM4dSpU84OuVaQEW8hhHAiGfEW9YHWms2bN+Pl5UXPnj0BSEpKYsKECfj5+VlVM4YPH17vq2a4uszMTOLj4zFNkzVr1lCaZ5Yub28YBuPHj6dFixZOjvTyyFQTpBMXQrguSbxFfRUXF8eMGTPYsWOHta9Zs2ZERUVhGAYRERFSotDFZWdnk5CQgGmarFq1ynrY1sPDgxEjRmAYBhMmTMDf39/JkVadJN5IJy6EcF2SeIv6btu2bdZc4a1btwLQs2dPfvzxR6tNQUEB3t7ezgpRXAG5ubkkJiZimiYrVqyguLgYAHd3d4YOHYphGEycOJGgoCAnR3pxkngjnbgQwnVJ4i3Er3bs2EFcXBwtW7bk/vvvB2DPnj307duXyMhIDMNg3LhxVgUV4ZqOHj1KUlISpmmWm+fv5uZGWFiYlYS3bt3ayZFeSBJvpBMXQrguSbyFuLh///vfVhIO4OPjQ3h4uDUdpVGjRk6MTlTXiRMnSE5OxjRNli5dyvnz5wF7PfEbb7wRwzCYNGkS7dq1c3KkdpJ4I524EMJ1uWrirZR6FLgP6An8V2t9X1VfK322+K32799v1Y9et26dtd/Pz4/s7Gw8PT2dGJ24Uv6/vXsPj6q+8zj+/pIEQrWESiHcby1YuQYBVwU0WxEfWAwiYxX7qFStSLH6bHFby2q91RXcsrtWqpTWYqW0RSZ4BZEtCy2bBREtF0MFRYFAgCBQLuGa5Ld/nMkQAkgmk5kzJ/m8fOZ5mHNOJp/z88xvvvnNOb9z4MAB3nzzTcLhMIsWLeL48ePRdZdffjmhUIhQKESnTp18y6jCG3XiIhJcAS68bwQqgOuApiq8JVm2bdsWnTWjXbt2zJ07F/DOA7/tttsYOXIkeXl5NG/e3OekEo9Dhw6xYMECwuEwCxcuPO3umAMHDiQUCjFmzBi+9rWvJTWXCm/UiYtIcAW18K5kZj8F2qvwFj+UlZWRnp4OwIIFCxg5ciRw6vb2oVCIUaNG0aJFCz9jSpxKS0t5++23CYfDvPXWW5SWlkbX9evXLzoS3r1794RnUeGNOnERCa6GUnib2T3APQAdO3bsv3Xr1iSkk4Zkz5495OfnM2/ePJYtWxadui4tLY1vfvOb5Ofn17u7KDZER44c4Z133iEcDvPmm29y6NCh6LrevXtHi/AePXok5PcH6s6VZtbEzF40s61mdsjM1pjZ8CrrrzGzj8zsiJktNTP/TuIREZE645yb6Zwb4Jwb0LJlS7/jSD3UsmVL7r33XpYsWcKuXbuYOXMmw4YNA6CoqOi0onvu3Lns2rXLr6gShy996UuMHj2aOXPmUFJSwhtvvMHtt99OVlYW69ev59FHH6Vnz5706NGDRx99lPXr15NKg8xJHfE2swuAfwFeArYBI4A/4F2ccxjYDNwNvAk8CQxxzl1+vtfViLdI/VfQuoCTu0+esTwjO4NBuwb5kKhupOKIt5ktA64+x+oC59zgKtvqVBNJaXv37mXr1q1ceumlAGzZsoUuXbpgZgwZMiQ6a0a7du18TirxOHHiBEuWLCEcDvPaa6+xb9++6Lru3btHR8JzcnLiujFT4E81MbN1wONAC2Ccc+7KyPILgM+Bfs65j77gJdSJizQAy2zZOdflutyk5ahrqVh4x0KFtwRNYWEhkydPZtGiRdGp6wAGDRrEmDFjuPvuu3VKSsCdPHmSpUuXEg6HefXVV/n888+j67p27RotwgcMGBBzER6oU02qM7NsoDtQCPQE1lauc86V4o2A9/QnnYiInIuZpZtZJpAGpJlZppml+51L5Hx69uzJ66+/zp49e5gzZw6jR48mMzOTgoICJk+efFohtn//fh+TSm1lZGQwbNgwZs6cyc6dO1myZAkTJkwgOzubTz/9lGeeeYbLLruMLl26MGnSJFauXBm9JiDRfBvxNrMM4G1gs3NuvJm9COxxzj1UZZsC4FfOuZfO8vO6UEekAdGId2oxs8eAR6stftw599j5flYj3pJqDh8+zMKFC9m2bRsPPvgg4J260Lp169NGSL/+9a/7nFTiUV5eTkFBAeFwmPz8fIqLi6Pr2rdvz5gxYwiFQlx55ZU0anT2selAnmpiZo2A3wPNgFHOuZNm9iyQ4Zz7XpXt1gOPOefyv+j11ImL1H8qvOsP9dkSBOvWrWPQoEEcPnw4uqxv377cdNNNhEIhLr74Yh/TSbwqKipYuXIl8+bNIxwOs3379ui6Nm3acOONNxIKhRgyZAhpaWnRdYErvM37Duc3QGdghHPuaGT5PcAdzrlBkecXAHuAS3WOt4io8K4/1GdLUBw9epTFixcTDod54403OHjwYHTdhg0buOSSS3xMJ3WloqKC9957j3A4TDgcZsuWLdF1rVq1YvTo0YRCIXJzc8nIyAhc4T0DyAGGOucOV1neEvgEuBNYgHfB5dWa1UREQLOa1CfqsyWIjh8/zp/+9CfC4TAbNmxg5cqV0fPBb7vtNjp37kwoFKJPnz5xzZoh/nLO8cEHHxAOh5k3bx6bN2+OrmvRogV79+4NTuEdmZd7C3AcKKuyarxzbo6ZDQWmA52Ad/FmOdlyvtdVJy4iQaXCWyR4nHPR4rqoqIiOHTtG13Xr1i16Tni/fv1UhAeYc45169ZFi/CNGzcCBKfwThR14iISVCq8RYKtrKyMZcuWEQ6HmT9/Pnv27Imu69KlC/PnzycnJ8fHhFIXnHMUFhbSu3fv4E4nKCIiIhJk6enpDB06lBkzZrBz506WLl3KxIkTad26NTt27KBr167RbefOnUtBQUHSpq6TumNm9OrVK+7XUeEtIiIiUgfS0tLIzc1l+vTp7Nixgw8++IBmzZoB3k1dJk6cyODBg+nQoQP3338/f/nLXygvL/c5tSSTCm8RERGROtaoUSN69jx1D8AjR45wxx130LFjR4qLi3nuuee4+uqrad++PRMnTuTjjz/2Ma0kiwpvERERkQTLyspi2rRpbNmyhVWrVvHDH/6Qrl27smvXLp5//nkOHToU3baoqIiTJ8+cxUmCT7f3FREREUkSM2PgwIEMHDiQKVOmsGbNGhYtWkS/fv2i24wdO5a//e1v3HDDDYRCIa655hoaN24c2y8qK4OiIiguhhMnoHFjaNsWOnSAdJV/ftGsJiIiPtKsJiJS1bFjx+jfvz8bNmyILsvKymLUqFGEQiGGDRtGkyZNzv0CzsGHH0LlqStVzyGvvANjt27QqxdoqsOYxdtn61QTERERkRSRmZlJYWEhhYWFPP744/Tu3ZsDBw7w8ssvk5eXxx//+Mdz/7BzUFDgFd3l5acX3XBq2ccfe9vVg8HXoFHhLSIiIpJievTowU9+8hPWrVvHRx99xFNPPcXAgQPJy8uLbvPggw9y8803Ew6HKS0t9Ua6S0rOLLirKy/3tvvwwwTvhVSnU01ERHykU01EpDYqKipo06YNJSUlADRt2pQRffsS+od/4J8uvZR197fn5IEzx1czsioY9Ku93pO0NMjL0znfMdCpJiIiIiINTKNGjXj33Xf52c9+xuWXX87Ro0fJX7mSsc8+S6u77+aNA++c9efOKMaLipKQViqp8BYREREJoM6dOzNp0iRWrFjBtvx8/mvcOAZ/4xscLyujE52i261gBYtYxCEOnf4C5eXerCeSNPpuQURERCTgOnzlKzwwYgQPjBhB8b59bLy3e3TdXOaylrWkkUZ/+nPP/1zKqAED+GqzZqD5wpNKhbeIiIhI0FWZ57vtRRexiVNTBV7DNaSRxhrWsIpVrJqxivGNGvGPPXvyg9tvZ3hurg+BGyYV3iIiIiJB17Yt7N591hlNro/893f+TgEFrO/73yz58EP+tH49t5SVRbcrKioiPT2dNm3aJDN5g6JzvEVERESCrkOH055mZFWcsUlzmnND1nAW/eu/svtXv2LWxInc8J3vRNdPnTqVdu3acdVVV/Hzn/+c7du3Jzx2Q6MRbxEREZGgS0/37kgZuXlOdMrAc7goK4tx48dDdnZ02YkTJ2jcuDHLly9n+fLlPPDAA1xxxRWEQiHGjBlDp06dvuAVpSY04i0iIiJSH/TqBa1anbo1/LmkpXnb9ep12uKZM2dSUlLC73//e2688UYyMzNZsWIFkyZN4tlnn41uVx/uAeMXFd4iIiIi9YEZDBrkjXynpZ1ZgKene8u6dfO2MzvjJZo1a8bYsWPJz89nz549vPLKK3zrW9/i5ptvjm7zy1/+kv79+/P000+zadOmRO9VvaI7V4qI+Eh3rhSRhCgr826OU1zsTRmYkeFdgNmhQ9x3qhw5ciQLFiyIPu/Tpw+hUIhQKMQll1wSb/KUFm+frcJbRMRHKrxFJGiOHTvG4sWLCYfDvP766xw8eDC67q677uLXv/61j+kSS7eMFxEREZGkyczMJC8vj5dffpmSkhIWLFjAuHHjaN68OZdddll0u/fff5+HH36YNWvW6LzwCBXeIiIiIlIrTZo0YcSIEcyaNYvdu3dz++23R9fNnj2bp556in79+tGtWzceeughVq9e3aCLcBXeIiIiIhK3xo0bk5mZGX1+0003ce+999KqVSs2b97M1KlTGThwIF26dGHKlCk+JvWPCm8RERERqXODBg3ihRdeoLi4mKVLlzJx4kRat27N1q1bKS4ujm63f/9+CgoKqKg486Y/9Y0KbxERERFJmLS0NHJzc5k+fTo7duxg+fLl3HfffdH1+fn5DB48mPbt2/P973+fP//5z5SXl/uYOHFUeIuIiIhIUjRq1IjBgwfTvXv36DIzo1OnTuzcuZPp06eTm5tL27ZtmTBhAkuXLvUxbd1T4S0iIiIivrnrrrv47LPPeO+99/jRj35E165dKSkpYcaMGTz55JPR7SoqKjh58qSPSeOnwltEREREfGVmDBgwgClTpvDJJ5/w17/+lcmTJzN+/PjoNqtWrSI7O5s777yThQsXcuLECR8T1058ty4SEREREalDZkZOTg45OTmnLV+6dCn79+9n1qxZzJo1i6ysLPLy8giFQgwbNuy0GVVSVcqNeJvZRWb2qpmVmtlWM7vV70wiInKKmTUxsxcjffQhM1tjZsP9ziUi9duPf/xjCgsLeeKJJ+jTpw8HDhxg9uzZjBo1ij59+gRifvCUK7yBXwAngGzg28ALZtbT30giIlJFOlAEXA1kAQ8Dr5hZZx8ziUgD0KNHDx555BHWrl3Lxo0bozfoGTp0KGYGwL59+7jllluYN28epaWlPic+naXSXwdmdgGwH+jlnNsUWTYb2OGce+hcPzdgwAC3evXqJKUUEak7Zva+c26A3zniZWbrgMedc/nn21Z9tojUtZMnT5KRkQHArFmzuPPOOwFo2rQpw4cPJxQKMXLkSL785S/H9Xvi7bNTbcS7O1BWWXRHrAU04i0ikqLMLBuv/y70O4uINEyVRTfAtddey7Rp07jiiis4evQo8+fP59Zbb6Vly5aMHj2asrIy33Km2sWVFwIHqy07AJzx54mZ3QPcE3l63Mw+THC2ZPgq8LnfIeqI9iX11Jf9gPq1Lxf7HSAeZpYBzAF+65z76Au2C0KfnarHlXLFRrli02ByHT9+nNdee+20Ir0W4uqzU63wPgw0q7asGXCo+obOuZnATAAzW11PvqqtF/sB2pdUVF/2A+rfvvidoTozW4Z3/vbZFDjnBke2awTMxrsu575zbA8Eo89WrtgoV2yUKzapnCuen0+1wnsTkG5m3ZxzH0eW9UVfX4qIJI1zLvd825h3FdOLeBfCj3DOBfuuFiIiSZBS53g750qB+cATZnaBmQ0CRuGNqIiISOp4AbgEuN45d9TvMCIiQZBShXfE94CmQAnwB2CCc+58I94zE54qOerLfoD2JRXVl/0A7YuvzKwTMB7IAXaZ2eHI49s1fIlU3Wflio1yxUa5YlMvc6XUdIIiIiIiIvVVKo54i4iIiIjUOyq8RURERESSINCFt5ldZGavmlmpmW01s1v9zlQbZnafma02s+Nm9pLfeWrLzJqY2YuR/xeHzGyNmQ33O1dtmdnvzGynmR00s01mdrffmeJhZt3M7JiZ/c7vLLVlZssi+1B5TvFGvzPFw8xuMbO/RfqwzWY2xO9Mda02/YKZ/bOZ7Yq8935jZk0SlK3Gfa+ZjTOz8irH3mEzy/U7V2T7ZLVXjT9zzewxMztZrb26JjOHeaaa2d7IY2pkNp6EiCFXwtrmHL8vluM8KcdSLLmS+d6L/L6Y+qxY2yzQhTfwC7z5Y7OBbwMvmFkQ73JZDPwU+I3fQeKUDhThzf+bBTwMvGJmnX3MFI+ngc7OuWZAHvBTM+vvc6Z4/AJ4z+8QdeA+59yFkUdgbz5jZtcCU4Hv4N0k7CrgU19DJUZM/YKZXQc8BFwDdAK6Ao8nKFusfe+KKsfehc65ZX7nSnJ7xfqZO7dae9XV8V3THPcAN+BNS9wHuB7vouBEiaV9EtU2Z1Oj4ynJx1KNc0Uk670HMfRZtWmzwBbeZnYBMAZ4xDl32Dn3v8AbwG3+Joudc26+c+41YK/fWeLhnCt1zj3mnNvinKtwzr0FfAYEslh1zhU6545XPo08vuZjpFozs1uAvwNL/M4iUY8DTzjnVkbeLzucczv8DlXXatEv3AG8GHn/7QeeBMYlKFtK9r0x5kpKe6XKZ26MOe4ApjnntkfeW9NI0LGUKu1zNjEcT0l778WYK6li7LNibrPAFt5Ad6DMObepyrK1QBBHvOslM8vG+/8U2BsgmdnzZnYE+AjYCSz0OVLMzKwZ8ATwA7+z1JGnzexzMytI5NeNiWRmacAAoKWZfWJm281supk19TtbotWgX+iJ15dXWgtkm1mLRGergX6RY2+TmT1iZqlwE7pktVdtPnOvN7N9ZlZoZhN8yHG2tklUjRBr+ySibeKl995ZnKfPirnNglx4XwgcrLbsAN5XtuIzM8sA5gC/dc595Hee2nLOfQ/vmBqCd3On41/8EynpSby/yLf7HaQO/Ajvq7x2eHOpvmlmQfwWIhvIAEJ4x1YO0A/vK816q4b9woV4fXmlyn/73bf/BegFtMIb2RwL/IuviTzJaq9YP3NfwbvBUkvgu8BPzGxsknOcrW0uTNB53rHkSlTbxEvvvWpq0GfF3GZBLrwPA82qLWsGHPIhi1RhZo3w7jZ6ArjP5zhxc86VR742bA+kyshEjZhZDjAU+E+/s9QF59y7zrlDzrnjzrnfAgXACL9z1ULlnR6fc87tdM59DvwHAdwX8y54ded4/G+V7WraL1Tv2yv/HVPfXtNcNeWc+9Q591nkq+f1eN8ihWJ9nbrORfLaK6bPXOfcBudccaT//D/gWWrRXmcRS46ztc1hl5gbmNQ4VwLbJl51cizVtbp678Wqhn1WzG2WCl+T1dYmIN3MujnnPo4s60uAT2uoDyIjCS/ijeiNcM6d9DlSXUoneOd45wKdgW2RQZ4LgTQz6+Gcu9THXHXFAQmbpSBRnHP7zWw7Xv7oYr/yxMM5l3u+bWLsFwrx+vJXIs/7ArudczGdB1qTXHGq1bGXgFxJaa/IOczxfObW1Xs1ls/+yrZZdZ7t6kI8NUmq9GN1ciwlQcLbK4Y+K+Y2C+yIt3OuFO+r/yfM7AIzGwSMwvvrJFDMLN3MMoE0vKIoM0XOHayNF/C+QrveOXf0fBunKjNrZd5UbxeaWVrkyuWxBO/ixJl4fyzkRB4zgAXAdX6Gqg0za25m11W+P8y7PflVwCK/s9XSLOD7kWPtK8A/A2/5nClRYukXXgbuMrMeZtYc7/SblxIRKpa+18yGR871xMy+ATwCvO53LpLUXrF+5prZKDP7inkuA+6nDtorxhwvAz8ws3Zm1haYRIKOpVhyJaptziWG4ylp771YciXzvVdFTfus2NvMORfYB3AR8BpQCmwDbvU7Uy334zFOzZpR+XjM71y12I9OkezH8L5+qXx82+9stdiXlsCf8WYCOQisB77rd6462K/HgN/5nSOO/yfv4X2F93dgJXCt37ni2J8M4PnIvuwCfg5k+p0rAfv5hf0C0DHyvGOVn/kBsDvy3psFNElQtnP2vdVzAT+LZCrFm/bxCSDD71xJbq9zfubiXatwuMrzP+DNVnEY7+L0+xOd4ywZDHgG2Bd5PANYAo/1muZKWNvEcjz5eSzFkiuZ773I7ztnn1UXbWaRHxIRERERkQQK7KkmIiIiIiJBosJbRERERCQJVHiLiIiIiCSBCm8RERERkSRQ4S0iIiIikgQqvEVEREREkkCFt4iIiIhIEqjwFhERERFJAhXe0uCZ2WIzc2Y2ptpyM7OXIuum+JVPREROUZ8tQaY7V0qDZ2Z9gQ+AjUBv51x5ZPk0vFvBznTOjfcxooiIRKjPliDTiLc0eM65tcBs4BLgNgAzm4zXgb8CTPAvnYiIVKU+W4JMI94igJl1ADYBu4BpwHPAO0Cec+6En9lEROR06rMlqDTiLQI454qA/wI643Xg/wfceLYO3My+Z2afmdkxM3vfzIYkN62ISMOmPluCSoW3yCl7qvz7LufckeobmNnNwLPAvwH98Dr7t82sY3IiiohIhPpsCRydaiICmNmtwO+A3UBrYIZz7ozzBM3sXWCdc+67VZZ9DISdcz9OVl4RkYZMfbYElUa8pcEzsxHAS8CHQB+8K+XvNrOLq23XGOgPLK72EouBKxOfVERE1GdLkKnwlgbNzAYDYWA7cJ1zbg/wMJAOTK22+VeBNLwRlqoqR1xERCSB1GdL0KnwlgbLzHKAt4ADwLXOuZ0AzrkwsBoYpYtwRERSg/psqQ9UeEuDZGZfBxYBDm/UZHO1TSrP/fv3Kss+B8qB7GrbZuNNaSUiIgmgPlvqC11cKRKDyIU6a51z91RZtgnI14U6IiKpRX22pJp0vwOIBMx/ALPNbBVQANwLtAVm+JpKRETORn22pBQV3iIxcM7NNbMWeBfztMG7qn6Ec26rv8lERKQ69dmSanSqiYiIiIhIEujiShERERGRJFDhLSIiIiKSBCq8RURERESSQIW3iIiIiEgSqPAWEREREUkCFd4iIiIiIkmgwltEREREJAlUeIuIiIiIJIEKbxERERGRJPh/pEW+vlXrTbAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x230.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aHqlGCGmRj7l",
        "colab_type": "text"
      },
      "source": [
        "# Sensitivity to outliers"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BD9qsAPXRj7m",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        },
        "outputId": "5a59aedd-0a6b-461d-e0bb-74744f5c3d2f"
      },
      "source": [
        "X_outliers = np.array([[3.4, 1.3], [3.2, 0.8]])\n",
        "y_outliers = np.array([0, 0])\n",
        "Xo1 = np.concatenate([X, X_outliers[:1]], axis=0)\n",
        "yo1 = np.concatenate([y, y_outliers[:1]], axis=0)\n",
        "Xo2 = np.concatenate([X, X_outliers[1:]], axis=0)\n",
        "yo2 = np.concatenate([y, y_outliers[1:]], axis=0)\n",
        "\n",
        "svm_clf2 = SVC(kernel=\"linear\", C=10**9)\n",
        "svm_clf2.fit(Xo2, yo2)\n",
        "\n",
        "plt.figure(figsize=(12,2.7))\n",
        "\n",
        "plt.subplot(121)\n",
        "plt.plot(Xo1[:, 0][yo1==1], Xo1[:, 1][yo1==1], \"bs\")\n",
        "plt.plot(Xo1[:, 0][yo1==0], Xo1[:, 1][yo1==0], \"yo\")\n",
        "plt.text(0.3, 1.0, \"Impossible!\", fontsize=24, color=\"red\")\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.annotate(\"Outlier\",\n",
        "             xy=(X_outliers[0][0], X_outliers[0][1]),\n",
        "             xytext=(2.5, 1.7),\n",
        "             ha=\"center\",\n",
        "             arrowprops=dict(facecolor='black', shrink=0.1),\n",
        "             fontsize=16,\n",
        "            )\n",
        "plt.axis([0, 5.5, 0, 2])\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.plot(Xo2[:, 0][yo2==1], Xo2[:, 1][yo2==1], \"bs\")\n",
        "plt.plot(Xo2[:, 0][yo2==0], Xo2[:, 1][yo2==0], \"yo\")\n",
        "plot_svc_decision_boundary(svm_clf2, 0, 5.5)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.annotate(\"Outlier\",\n",
        "             xy=(X_outliers[1][0], X_outliers[1][1]),\n",
        "             xytext=(3.2, 0.08),\n",
        "             ha=\"center\",\n",
        "             arrowprops=dict(facecolor='black', shrink=0.1),\n",
        "             fontsize=16,\n",
        "            )\n",
        "plt.axis([0, 5.5, 0, 2])\n",
        "\n",
        "# save_fig(\"sensitivity_to_outliers_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x194.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cGoI6BQVRj7o",
        "colab_type": "text"
      },
      "source": [
        "# Large margin *vs* margin violations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9a2OR8KCRj7p",
        "colab_type": "text"
      },
      "source": [
        "This is the first code example in chapter 5:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nQ4O2Rk9Rj7q",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "40e601f0-1d7b-4e43-f3d1-cf90ec84f204"
      },
      "source": [
        "import numpy as np\n",
        "from sklearn import datasets\n",
        "from sklearn.pipeline import Pipeline\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.svm import LinearSVC\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
        "y = (iris[\"target\"] == 2).astype(np.float64)  # Iris-Virginica\n",
        "\n",
        "svm_clf = Pipeline([\n",
        "        (\"scaler\", StandardScaler()),\n",
        "        (\"linear_svc\", LinearSVC(C=1, loss=\"hinge\", random_state=42)),\n",
        "    ])\n",
        "\n",
        "svm_clf.fit(X, y)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('linear_svc',\n",
              "                 LinearSVC(C=1, class_weight=None, dual=True,\n",
              "                           fit_intercept=True, intercept_scaling=1,\n",
              "                           loss='hinge', max_iter=1000, multi_class='ovr',\n",
              "                           penalty='l2', random_state=42, tol=0.0001,\n",
              "                           verbose=0))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "st5oWmAFRj7s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "4b937930-5f66-4aa6-f667-54c199a0df38"
      },
      "source": [
        "svm_clf.predict([[5.5, 1.7]])"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4TrDGteZRj7u",
        "colab_type": "text"
      },
      "source": [
        "Now let's generate the graph comparing different regularization settings:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cr3s2y9eRj7v",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "ba89b389-684a-4307-8ee2-af59d96c75a5"
      },
      "source": [
        "scaler = StandardScaler()\n",
        "svm_clf1 = LinearSVC(C=1, loss=\"hinge\", random_state=42)\n",
        "svm_clf2 = LinearSVC(C=100, loss=\"hinge\", random_state=42)\n",
        "\n",
        "scaled_svm_clf1 = Pipeline([\n",
        "        (\"scaler\", scaler),\n",
        "        (\"linear_svc\", svm_clf1),\n",
        "    ])\n",
        "scaled_svm_clf2 = Pipeline([\n",
        "        (\"scaler\", scaler),\n",
        "        (\"linear_svc\", svm_clf2),\n",
        "    ])\n",
        "\n",
        "scaled_svm_clf1.fit(X, y)\n",
        "scaled_svm_clf2.fit(X, y)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('linear_svc',\n",
              "                 LinearSVC(C=100, class_weight=None, dual=True,\n",
              "                           fit_intercept=True, intercept_scaling=1,\n",
              "                           loss='hinge', max_iter=1000, multi_class='ovr',\n",
              "                           penalty='l2', random_state=42, tol=0.0001,\n",
              "                           verbose=0))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M6MnrdJqRj7x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Convert to unscaled parameters\n",
        "b1 = svm_clf1.decision_function([-scaler.mean_ / scaler.scale_])\n",
        "b2 = svm_clf2.decision_function([-scaler.mean_ / scaler.scale_])\n",
        "w1 = svm_clf1.coef_[0] / scaler.scale_\n",
        "w2 = svm_clf2.coef_[0] / scaler.scale_\n",
        "svm_clf1.intercept_ = np.array([b1])\n",
        "svm_clf2.intercept_ = np.array([b2])\n",
        "svm_clf1.coef_ = np.array([w1])\n",
        "svm_clf2.coef_ = np.array([w2])\n",
        "\n",
        "# Find support vectors (LinearSVC does not do this automatically)\n",
        "t = y * 2 - 1\n",
        "support_vectors_idx1 = (t * (X.dot(w1) + b1) < 1).ravel()\n",
        "support_vectors_idx2 = (t * (X.dot(w2) + b2) < 1).ravel()\n",
        "svm_clf1.support_vectors_ = X[support_vectors_idx1]\n",
        "svm_clf2.support_vectors_ = X[support_vectors_idx2]"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lMHQiMfDFOUH",
        "colab_type": "text"
      },
      "source": [
        "# Using C to control the trade-offs for soft margin "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QFI46Li5Rj70",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "e352fc7d-2620-4dd6-c8a4-133460566bbe"
      },
      "source": [
        "plt.figure(figsize=(12,3.2))\n",
        "plt.subplot(121)\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\", label=\"Iris-Virginica\")\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\", label=\"Iris-Versicolor\")\n",
        "plot_svc_decision_boundary(svm_clf1, 4, 6)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.legend(loc=\"upper left\", fontsize=14)\n",
        "plt.title(\"$C = {}$\".format(svm_clf1.C), fontsize=16)\n",
        "plt.axis([4, 6, 0.8, 2.8])\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
        "plot_svc_decision_boundary(svm_clf2, 4, 6)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.title(\"$C = {}$\".format(svm_clf2.C), fontsize=16)\n",
        "plt.axis([4, 6, 0.8, 2.8])\n",
        "\n",
        "# save_fig(\"regularization_plot\")"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4.0, 6.0, 0.8, 2.8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x230.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "8UfQorPGRj72",
        "colab_type": "text"
      },
      "source": [
        "# Non-linear classification"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U1QW5o3MRj73",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "outputId": "6684bc30-0fc3-43fa-c39e-c14524fc9518"
      },
      "source": [
        "X1D = np.linspace(-4, 4, 9).reshape(-1, 1)\n",
        "X2D = np.c_[X1D, X1D**2]\n",
        "y = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])\n",
        "\n",
        "plt.figure(figsize=(11, 4))\n",
        "\n",
        "plt.subplot(121)\n",
        "plt.grid(True, which='both')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.plot(X1D[:, 0][y==0], np.zeros(4), \"bs\")\n",
        "plt.plot(X1D[:, 0][y==1], np.zeros(5), \"g^\")\n",
        "plt.gca().get_yaxis().set_ticks([])\n",
        "plt.xlabel(r\"$x_1$\", fontsize=20)\n",
        "plt.axis([-4.5, 4.5, -0.2, 0.2])\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.grid(True, which='both')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.axvline(x=0, color='k')\n",
        "plt.plot(X2D[:, 0][y==0], X2D[:, 1][y==0], \"bs\")\n",
        "plt.plot(X2D[:, 0][y==1], X2D[:, 1][y==1], \"g^\")\n",
        "plt.xlabel(r\"$x_1$\", fontsize=20)\n",
        "plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n",
        "plt.gca().get_yaxis().set_ticks([0, 4, 8, 12, 16])\n",
        "plt.plot([-4.5, 4.5], [6.5, 6.5], \"r--\", linewidth=3)\n",
        "plt.axis([-4.5, 4.5, -1, 17])\n",
        "\n",
        "plt.subplots_adjust(right=1)\n",
        "\n",
        "# save_fig(\"higher_dimensions_plot\", tight_layout=False)\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 792x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jj4bnoK_HUrP",
        "colab_type": "text"
      },
      "source": [
        "# moon data set with polynomial features"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v1-M_HVMRj75",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "e7534484-2c44-4541-de88-c9e1da6294c1"
      },
      "source": [
        "from sklearn.datasets import make_moons\n",
        "X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
        "\n",
        "def plot_dataset(X, y, axes):\n",
        "    plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
        "    plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
        "    plt.axis(axes)\n",
        "    plt.grid(True, which='both')\n",
        "    plt.xlabel(r\"$x_1$\", fontsize=20)\n",
        "    plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n",
        "\n",
        "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "un-Fn0-5HSVW",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "REaNS7Y5Rj77",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "0cc596bf-39b7-4006-f80e-746b01be8ab1"
      },
      "source": [
        "from sklearn.datasets import make_moons\n",
        "from sklearn.pipeline import Pipeline\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "\n",
        "polynomial_svm_clf = Pipeline([\n",
        "        (\"poly_features\", PolynomialFeatures(degree=3)),\n",
        "        (\"scaler\", StandardScaler()),\n",
        "        (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\", random_state=42))\n",
        "    ])\n",
        "\n",
        "polynomial_svm_clf.fit(X, y)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('poly_features',\n",
              "                 PolynomialFeatures(degree=3, include_bias=True,\n",
              "                                    interaction_only=False, order='C')),\n",
              "                ('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('svm_clf',\n",
              "                 LinearSVC(C=10, class_weight=None, dual=True,\n",
              "                           fit_intercept=True, intercept_scaling=1,\n",
              "                           loss='hinge', max_iter=1000, multi_class='ovr',\n",
              "                           penalty='l2', random_state=42, tol=0.0001,\n",
              "                           verbose=0))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mNpPpDy0Rj7-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "37e32b34-ff67-4408-e197-c9c13c4e1436"
      },
      "source": [
        "def plot_predictions(clf, axes):\n",
        "    x0s = np.linspace(axes[0], axes[1], 100)\n",
        "    x1s = np.linspace(axes[2], axes[3], 100)\n",
        "    x0, x1 = np.meshgrid(x0s, x1s)\n",
        "    X = np.c_[x0.ravel(), x1.ravel()]\n",
        "    y_pred = clf.predict(X).reshape(x0.shape)\n",
        "    y_decision = clf.decision_function(X).reshape(x0.shape)\n",
        "    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n",
        "    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)\n",
        "\n",
        "plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
        "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
        "\n",
        "# save_fig(\"moons_polynomial_svc_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BLlvIreoIZkv",
        "colab_type": "text"
      },
      "source": [
        "# KErnel Trick - Polynomial Kernel"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TnCI9-s_Rj8A",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "167073f6-2624-42f9-9e38-f0af9f5f3cd3"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "\n",
        "poly_kernel_svm_clf = Pipeline([\n",
        "        (\"scaler\", StandardScaler()),\n",
        "        (\"svm_clf\", SVC(kernel=\"poly\", degree=3, coef0=1, C=5))\n",
        "    ])\n",
        "poly_kernel_svm_clf.fit(X, y)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('svm_clf',\n",
              "                 SVC(C=5, break_ties=False, cache_size=200, class_weight=None,\n",
              "                     coef0=1, decision_function_shape='ovr', degree=3,\n",
              "                     gamma='scale', kernel='poly', max_iter=-1,\n",
              "                     probability=False, random_state=None, shrinking=True,\n",
              "                     tol=0.001, verbose=False))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x1AndrOIRj8F",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "b8ffead6-1cd0-48f1-ef6a-0a71687b6a30"
      },
      "source": [
        "poly100_kernel_svm_clf = Pipeline([\n",
        "        (\"scaler\", StandardScaler()),\n",
        "        (\"svm_clf\", SVC(kernel=\"poly\", degree=10, coef0=100, C=5))\n",
        "    ])\n",
        "poly100_kernel_svm_clf.fit(X, y)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('svm_clf',\n",
              "                 SVC(C=5, break_ties=False, cache_size=200, class_weight=None,\n",
              "                     coef0=100, decision_function_shape='ovr', degree=10,\n",
              "                     gamma='scale', kernel='poly', max_iter=-1,\n",
              "                     probability=False, random_state=None, shrinking=True,\n",
              "                     tol=0.001, verbose=False))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7vSObpbKRj8H",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "99517a4a-9bdb-401c-b2e0-aa2a01b48804"
      },
      "source": [
        "plt.figure(figsize=(11, 4))\n",
        "\n",
        "plt.subplot(121)\n",
        "plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
        "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
        "plt.title(r\"$d=3, r=1, C=5$\", fontsize=18)\n",
        "\n",
        "plt.subplot(122)\n",
        "plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
        "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
        "plt.title(r\"$d=10, r=100, C=5$\", fontsize=18)\n",
        "\n",
        "# save_fig(\"moons_kernelized_polynomial_svc_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FchhxW1LJaZL",
        "colab_type": "text"
      },
      "source": [
        "# Adding Similarity Features"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "SSKpJIqLRj8J",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "outputId": "eff989c1-65de-4bc7-9eaa-7af16f89eecb"
      },
      "source": [
        "def gaussian_rbf(x, landmark, gamma):\n",
        "    return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1)**2)\n",
        "\n",
        "gamma = 0.3\n",
        "\n",
        "x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)\n",
        "x2s = gaussian_rbf(x1s, -2, gamma)\n",
        "x3s = gaussian_rbf(x1s, 1, gamma)\n",
        "\n",
        "XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]\n",
        "yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])\n",
        "\n",
        "plt.figure(figsize=(11, 4))\n",
        "\n",
        "plt.subplot(121)\n",
        "plt.grid(True, which='both')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c=\"red\")\n",
        "plt.plot(X1D[:, 0][yk==0], np.zeros(4), \"bs\")\n",
        "plt.plot(X1D[:, 0][yk==1], np.zeros(5), \"g^\")\n",
        "plt.plot(x1s, x2s, \"g--\")\n",
        "plt.plot(x1s, x3s, \"b:\")\n",
        "plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])\n",
        "plt.xlabel(r\"$x_1$\", fontsize=20)\n",
        "plt.ylabel(r\"Similarity\", fontsize=14)\n",
        "plt.annotate(r'$\\mathbf{x}$',\n",
        "             xy=(X1D[3, 0], 0),\n",
        "             xytext=(-0.5, 0.20),\n",
        "             ha=\"center\",\n",
        "             arrowprops=dict(facecolor='black', shrink=0.1),\n",
        "             fontsize=18,\n",
        "            )\n",
        "plt.text(-2, 0.9, \"$x_2$\", ha=\"center\", fontsize=20)\n",
        "plt.text(1, 0.9, \"$x_3$\", ha=\"center\", fontsize=20)\n",
        "plt.axis([-4.5, 4.5, -0.1, 1.1])\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.grid(True, which='both')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.axvline(x=0, color='k')\n",
        "plt.plot(XK[:, 0][yk==0], XK[:, 1][yk==0], \"bs\")\n",
        "plt.plot(XK[:, 0][yk==1], XK[:, 1][yk==1], \"g^\")\n",
        "plt.xlabel(r\"$x_2$\", fontsize=20)\n",
        "plt.ylabel(r\"$x_3$  \", fontsize=20, rotation=0)\n",
        "plt.annotate(r'$\\phi\\left(\\mathbf{x}\\right)$',\n",
        "             xy=(XK[3, 0], XK[3, 1]),\n",
        "             xytext=(0.65, 0.50),\n",
        "             ha=\"center\",\n",
        "             arrowprops=dict(facecolor='black', shrink=0.1),\n",
        "             fontsize=18,\n",
        "            )\n",
        "plt.plot([-0.1, 1.1], [0.57, -0.1], \"r--\", linewidth=3)\n",
        "plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
        "    \n",
        "plt.subplots_adjust(right=1)\n",
        "\n",
        "# save_fig(\"kernel_method_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5bqljqa3Rj8M",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "be0f62e9-1323-4450-c4d8-97a7533f9e33"
      },
      "source": [
        "x1_example = X1D[3, 0]\n",
        "for landmark in (-2, 1):\n",
        "    k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)\n",
        "    print(\"Phi({}, {}) = {}\".format(x1_example, landmark, k))"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Phi(-1.0, -2) = [0.74081822]\n",
            "Phi(-1.0, 1) = [0.30119421]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I2qN3tF6Rj8O",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "ced6e25d-3977-4a46-cca4-796c99ef9aba"
      },
      "source": [
        "rbf_kernel_svm_clf = Pipeline([\n",
        "        (\"scaler\", StandardScaler()),\n",
        "        (\"svm_clf\", SVC(kernel=\"rbf\", gamma=5, C=0.001))\n",
        "    ])\n",
        "rbf_kernel_svm_clf.fit(X, y)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('scaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('svm_clf',\n",
              "                 SVC(C=0.001, break_ties=False, cache_size=200,\n",
              "                     class_weight=None, coef0=0.0,\n",
              "                     decision_function_shape='ovr', degree=3, gamma=5,\n",
              "                     kernel='rbf', max_iter=-1, probability=False,\n",
              "                     random_state=None, shrinking=True, tol=0.001,\n",
              "                     verbose=False))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "fhMk63CyRj8Q",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 474
        },
        "outputId": "56b7a8a1-2e47-442a-9fbd-b9445301be99"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "\n",
        "gamma1, gamma2 = 0.1, 5\n",
        "C1, C2 = 0.001, 1000\n",
        "hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n",
        "\n",
        "svm_clfs = []\n",
        "for gamma, C in hyperparams:\n",
        "    rbf_kernel_svm_clf = Pipeline([\n",
        "            (\"scaler\", StandardScaler()),\n",
        "            (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n",
        "        ])\n",
        "    rbf_kernel_svm_clf.fit(X, y)\n",
        "    svm_clfs.append(rbf_kernel_svm_clf)\n",
        "\n",
        "plt.figure(figsize=(11, 7))\n",
        "\n",
        "for i, svm_clf in enumerate(svm_clfs):\n",
        "    plt.subplot(221 + i)\n",
        "    plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])\n",
        "    plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
        "    gamma, C = hyperparams[i]\n",
        "    plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)\n",
        "\n",
        "# save_fig(\"moons_rbf_svc_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x504 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fLYQuHwYRj8S",
        "colab_type": "text"
      },
      "source": [
        "# Regression\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hn_ZKmTuRj8S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(42)\n",
        "m = 50\n",
        "X = 2 * np.random.rand(m, 1)\n",
        "y = (4 + 3 * X + np.random.randn(m, 1)).ravel()"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v7YLmF3hNmai",
        "colab_type": "text"
      },
      "source": [
        "# linear"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tBCNZXJHRj8V",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "72eff1c3-7d90-4d13-dd37-6d20dbd2c005"
      },
      "source": [
        "from sklearn.svm import LinearSVR\n",
        "\n",
        "svm_reg = LinearSVR(epsilon=1.5, random_state=42)\n",
        "svm_reg.fit(X, y)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearSVR(C=1.0, dual=True, epsilon=1.5, fit_intercept=True,\n",
              "          intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,\n",
              "          random_state=42, tol=0.0001, verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kQLqFqIyRj8Y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)\n",
        "svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)\n",
        "svm_reg1.fit(X, y)\n",
        "svm_reg2.fit(X, y)\n",
        "\n",
        "def find_support_vectors(svm_reg, X, y):\n",
        "    y_pred = svm_reg.predict(X)\n",
        "    off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)\n",
        "    return np.argwhere(off_margin)\n",
        "\n",
        "svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)\n",
        "svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)\n",
        "\n",
        "eps_x1 = 1\n",
        "eps_y_pred = svm_reg1.predict([[eps_x1]])"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fFu0Wm2oRj8a",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 310
        },
        "outputId": "7774231c-2e90-4be0-bc67-1254cb1a2304"
      },
      "source": [
        "def plot_svm_regression(svm_reg, X, y, axes):\n",
        "    x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n",
        "    y_pred = svm_reg.predict(x1s)\n",
        "    plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
        "    plt.plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n",
        "    plt.plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n",
        "    plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')\n",
        "    plt.plot(X, y, \"bo\")\n",
        "    plt.xlabel(r\"$x_1$\", fontsize=18)\n",
        "    plt.legend(loc=\"upper left\", fontsize=18)\n",
        "    plt.axis(axes)\n",
        "\n",
        "plt.figure(figsize=(9, 4))\n",
        "plt.subplot(121)\n",
        "plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])\n",
        "plt.title(r\"$\\epsilon = {}$\".format(svm_reg1.epsilon), fontsize=18)\n",
        "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n",
        "#plt.plot([eps_x1, eps_x1], [eps_y_pred, eps_y_pred - svm_reg1.epsilon], \"k-\", linewidth=2)\n",
        "plt.annotate(\n",
        "        '', xy=(eps_x1, eps_y_pred), xycoords='data',\n",
        "        xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),\n",
        "        textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n",
        "    )\n",
        "plt.text(0.91, 5.6, r\"$\\epsilon$\", fontsize=20)\n",
        "plt.subplot(122)\n",
        "plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])\n",
        "plt.title(r\"$\\epsilon = {}$\".format(svm_reg2.epsilon), fontsize=18)\n",
        "# save_fig(\"svm_regression_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rTZIVmb4Rj8c",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(42)\n",
        "m = 100\n",
        "X = 2 * np.random.rand(m, 1) - 1\n",
        "y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p4I4lst3Rj8e",
        "colab_type": "text"
      },
      "source": [
        "**Warning**: the default value of `gamma` will change from `'auto'` to `'scale'` in version 0.22 to better account for unscaled features. To preserve the same results as in the book, we explicitly set it to `'auto'`, but you should probably just use the default in your own code."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lk5a3hpQObsp",
        "colab_type": "text"
      },
      "source": [
        "# nonlinear with kernel"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "55Np_ivSRj8e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "ce1ec086-0ece-47aa-a5c4-0fdd02eb594f"
      },
      "source": [
        "from sklearn.svm import SVR\n",
        "\n",
        "svm_poly_reg = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1, gamma=\"auto\")\n",
        "svm_poly_reg.fit(X, y)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVR(C=100, cache_size=200, coef0=0.0, degree=2, epsilon=0.1, gamma='auto',\n",
              "    kernel='poly', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "apH8B-8jRj8g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "142e6ab9-ae84-4269-ebaf-40e52308913e"
      },
      "source": [
        "from sklearn.svm import SVR\n",
        "\n",
        "svm_poly_reg1 = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1, gamma=\"auto\")\n",
        "svm_poly_reg2 = SVR(kernel=\"poly\", degree=2, C=0.01, epsilon=0.1, gamma=\"auto\")\n",
        "svm_poly_reg1.fit(X, y)\n",
        "svm_poly_reg2.fit(X, y)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVR(C=0.01, cache_size=200, coef0=0.0, degree=2, epsilon=0.1, gamma='auto',\n",
              "    kernel='poly', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YIHpyULRRj8j",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "81ceaf58-db54-407c-fc8f-2590ca0bd8ec"
      },
      "source": [
        "plt.figure(figsize=(9, 4))\n",
        "plt.subplot(121)\n",
        "plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])\n",
        "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg1.degree, svm_poly_reg1.C, svm_poly_reg1.epsilon), fontsize=18)\n",
        "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n",
        "plt.subplot(122)\n",
        "plot_svm_regression(svm_poly_reg2, X, y, [-1, 1, 0, 1])\n",
        "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg2.degree, svm_poly_reg2.C, svm_poly_reg2.epsilon), fontsize=18)\n",
        "# save_fig(\"svm_with_polynomial_kernel_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jNvZkqfMRj8l",
        "colab_type": "text"
      },
      "source": [
        "# Under the hood"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NNjOfeamRj8l",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
        "y = (iris[\"target\"] == 2).astype(np.float64)  # Iris-Virginica"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnUx492qRj8n",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        },
        "outputId": "f945ea1c-2a94-4925-c858-87eb42d7628b"
      },
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "def plot_3D_decision_function(ax, w, b, x1_lim=[4, 6], x2_lim=[0.8, 2.8]):\n",
        "    x1_in_bounds = (X[:, 0] > x1_lim[0]) & (X[:, 0] < x1_lim[1])\n",
        "    X_crop = X[x1_in_bounds]\n",
        "    y_crop = y[x1_in_bounds]\n",
        "    x1s = np.linspace(x1_lim[0], x1_lim[1], 20)\n",
        "    x2s = np.linspace(x2_lim[0], x2_lim[1], 20)\n",
        "    x1, x2 = np.meshgrid(x1s, x2s)\n",
        "    xs = np.c_[x1.ravel(), x2.ravel()]\n",
        "    df = (xs.dot(w) + b).reshape(x1.shape)\n",
        "    m = 1 / np.linalg.norm(w)\n",
        "    boundary_x2s = -x1s*(w[0]/w[1])-b/w[1]\n",
        "    margin_x2s_1 = -x1s*(w[0]/w[1])-(b-1)/w[1]\n",
        "    margin_x2s_2 = -x1s*(w[0]/w[1])-(b+1)/w[1]\n",
        "    ax.plot_surface(x1s, x2, np.zeros_like(x1),\n",
        "                    color=\"b\", alpha=0.2, cstride=100, rstride=100)\n",
        "    ax.plot(x1s, boundary_x2s, 0, \"k-\", linewidth=2, label=r\"$h=0$\")\n",
        "    ax.plot(x1s, margin_x2s_1, 0, \"k--\", linewidth=2, label=r\"$h=\\pm 1$\")\n",
        "    ax.plot(x1s, margin_x2s_2, 0, \"k--\", linewidth=2)\n",
        "    ax.plot(X_crop[:, 0][y_crop==1], X_crop[:, 1][y_crop==1], 0, \"g^\")\n",
        "    ax.plot_wireframe(x1, x2, df, alpha=0.3, color=\"k\")\n",
        "    ax.plot(X_crop[:, 0][y_crop==0], X_crop[:, 1][y_crop==0], 0, \"bs\")\n",
        "    ax.axis(x1_lim + x2_lim)\n",
        "    ax.text(4.5, 2.5, 3.8, \"Decision function $h$\", fontsize=15)\n",
        "    ax.set_xlabel(r\"Petal length\", fontsize=15)\n",
        "    ax.set_ylabel(r\"Petal width\", fontsize=15)\n",
        "    ax.set_zlabel(r\"$h = \\mathbf{w}^T \\mathbf{x} + b$\", fontsize=18)\n",
        "    ax.legend(loc=\"upper left\", fontsize=16)\n",
        "\n",
        "fig = plt.figure(figsize=(11, 6))\n",
        "ax1 = fig.add_subplot(111, projection='3d')\n",
        "plot_3D_decision_function(ax1, w=svm_clf2.coef_[0], b=svm_clf2.intercept_[0])\n",
        "\n",
        "#save_fig(\"iris_3D_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "24urxzHgRj8p",
        "colab_type": "text"
      },
      "source": [
        "# Small weight vector results in a large margin"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cSLQ5U71Rj8p",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "d16254d7-b322-49d8-8233-ca70bf8dc241"
      },
      "source": [
        "def plot_2D_decision_function(w, b, ylabel=True, x1_lim=[-3, 3]):\n",
        "    x1 = np.linspace(x1_lim[0], x1_lim[1], 200)\n",
        "    y = w * x1 + b\n",
        "    m = 1 / w\n",
        "\n",
        "    plt.plot(x1, y)\n",
        "    plt.plot(x1_lim, [1, 1], \"k:\")\n",
        "    plt.plot(x1_lim, [-1, -1], \"k:\")\n",
        "    plt.axhline(y=0, color='k')\n",
        "    plt.axvline(x=0, color='k')\n",
        "    plt.plot([m, m], [0, 1], \"k--\")\n",
        "    plt.plot([-m, -m], [0, -1], \"k--\")\n",
        "    plt.plot([-m, m], [0, 0], \"k-o\", linewidth=3)\n",
        "    plt.axis(x1_lim + [-2, 2])\n",
        "    plt.xlabel(r\"$x_1$\", fontsize=16)\n",
        "    if ylabel:\n",
        "        plt.ylabel(r\"$w_1 x_1$  \", rotation=0, fontsize=16)\n",
        "    plt.title(r\"$w_1 = {}$\".format(w), fontsize=16)\n",
        "\n",
        "plt.figure(figsize=(12, 3.2))\n",
        "plt.subplot(121)\n",
        "plot_2D_decision_function(1, 0)\n",
        "plt.subplot(122)\n",
        "plot_2D_decision_function(0.5, 0, ylabel=False)\n",
        "# save_fig(\"small_w_large_margin_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x230.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wr5SAJQSRj8r",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "701274f7-e453-4f90-ec54-a84f0b90af91"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "from sklearn import datasets\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
        "y = (iris[\"target\"] == 2).astype(np.float64) # Iris-Virginica\n",
        "\n",
        "svm_clf = SVC(kernel=\"linear\", C=1)\n",
        "svm_clf.fit(X, y)\n",
        "svm_clf.predict([[5.3, 1.3]])"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ivXZZswlRj8u",
        "colab_type": "text"
      },
      "source": [
        "# Hinge loss"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2hrBerA2Rj8u",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 223
        },
        "outputId": "3a4d694e-0701-498c-9d42-30709a677704"
      },
      "source": [
        "t = np.linspace(-2, 4, 200)\n",
        "h = np.where(1 - t < 0, 0, 1 - t)  # max(0, 1-t)\n",
        "\n",
        "plt.figure(figsize=(5,2.8))\n",
        "plt.plot(t, h, \"b-\", linewidth=2, label=\"$max(0, 1 - t)$\")\n",
        "plt.grid(True, which='both')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.axvline(x=0, color='k')\n",
        "plt.yticks(np.arange(-1, 2.5, 1))\n",
        "plt.xlabel(\"$t$\", fontsize=16)\n",
        "plt.axis([-2, 4, -1, 2.5])\n",
        "plt.legend(loc=\"upper right\", fontsize=16)\n",
        "# save_fig(\"hinge_plot\")\n",
        "plt.show()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x201.6 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ad4G0vERj8x",
        "colab_type": "text"
      },
      "source": [
        "# Extra material"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ydOmKv9Rj8x",
        "colab_type": "text"
      },
      "source": [
        "## Training time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YKkAbM0iRj8y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "e43b0009-572b-41d8-f34f-547597b22325"
      },
      "source": [
        "X, y = make_moons(n_samples=1000, noise=0.4, random_state=42)\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fc79c7089b0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-uc50qBURj80",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        },
        "outputId": "a0cc0558-c4d4-4732-82f9-0a9cc9f925c9"
      },
      "source": [
        "import time\n",
        "\n",
        "tol = 0.1\n",
        "tols = []\n",
        "times = []\n",
        "for i in range(10):\n",
        "    svm_clf = SVC(kernel=\"poly\", gamma=3, C=10, tol=tol, verbose=1)\n",
        "    t1 = time.time()\n",
        "    svm_clf.fit(X, y)\n",
        "    t2 = time.time()\n",
        "    times.append(t2-t1)\n",
        "    tols.append(tol)\n",
        "    print(i, tol, t2-t1)\n",
        "    tol /= 10\n",
        "plt.semilogx(tols, times)"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[LibSVM]0 0.1 0.38090014457702637\n",
            "[LibSVM]1 0.01 0.39180684089660645\n",
            "[LibSVM]2 0.001 0.47606778144836426\n",
            "[LibSVM]3 0.0001 1.0549778938293457\n",
            "[LibSVM]4 1e-05 1.9176898002624512\n",
            "[LibSVM]5 1.0000000000000002e-06 1.706273078918457\n",
            "[LibSVM]6 1.0000000000000002e-07 13.618587255477905\n",
            "[LibSVM]7 1.0000000000000002e-08 1.8740930557250977\n",
            "[LibSVM]8 1.0000000000000003e-09 1.941359043121338\n",
            "[LibSVM]9 1.0000000000000003e-10 1.694249153137207\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fc7997f9ef0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p3BtEd6jRj82",
        "colab_type": "text"
      },
      "source": [
        "## Linear SVM classifier implementation using Batch Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9x8wfT0bRj82",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Training set\n",
        "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
        "y = (iris[\"target\"] == 2).astype(np.float64).reshape(-1, 1) # Iris-Virginica"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ia9bwcxMRj84",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "e40fa370-d7fe-4b48-af74-5dc709db440b"
      },
      "source": [
        "from sklearn.base import BaseEstimator\n",
        "\n",
        "class MyLinearSVC(BaseEstimator):\n",
        "    def __init__(self, C=1, eta0=1, eta_d=10000, n_epochs=1000, random_state=None):\n",
        "        self.C = C\n",
        "        self.eta0 = eta0\n",
        "        self.n_epochs = n_epochs\n",
        "        self.random_state = random_state\n",
        "        self.eta_d = eta_d\n",
        "\n",
        "    def eta(self, epoch):\n",
        "        return self.eta0 / (epoch + self.eta_d)\n",
        "        \n",
        "    def fit(self, X, y):\n",
        "        # Random initialization\n",
        "        if self.random_state:\n",
        "            np.random.seed(self.random_state)\n",
        "        w = np.random.randn(X.shape[1], 1) # n feature weights\n",
        "        b = 0\n",
        "\n",
        "        m = len(X)\n",
        "        t = y * 2 - 1  # -1 if t==0, +1 if t==1\n",
        "        X_t = X * t\n",
        "        self.Js=[]\n",
        "\n",
        "        # Training\n",
        "        for epoch in range(self.n_epochs):\n",
        "            support_vectors_idx = (X_t.dot(w) + t * b < 1).ravel()\n",
        "            X_t_sv = X_t[support_vectors_idx]\n",
        "            t_sv = t[support_vectors_idx]\n",
        "\n",
        "            J = 1/2 * np.sum(w * w) + self.C * (np.sum(1 - X_t_sv.dot(w)) - b * np.sum(t_sv))\n",
        "            self.Js.append(J)\n",
        "\n",
        "            w_gradient_vector = w - self.C * np.sum(X_t_sv, axis=0).reshape(-1, 1)\n",
        "            b_derivative = -C * np.sum(t_sv)\n",
        "                \n",
        "            w = w - self.eta(epoch) * w_gradient_vector\n",
        "            b = b - self.eta(epoch) * b_derivative\n",
        "            \n",
        "\n",
        "        self.intercept_ = np.array([b])\n",
        "        self.coef_ = np.array([w])\n",
        "        support_vectors_idx = (X_t.dot(w) + t * b < 1).ravel()\n",
        "        self.support_vectors_ = X[support_vectors_idx]\n",
        "        return self\n",
        "\n",
        "    def decision_function(self, X):\n",
        "        return X.dot(self.coef_[0]) + self.intercept_[0]\n",
        "\n",
        "    def predict(self, X):\n",
        "        return (self.decision_function(X) >= 0).astype(np.float64)\n",
        "\n",
        "C=2\n",
        "svm_clf = MyLinearSVC(C=C, eta0 = 10, eta_d = 1000, n_epochs=60000, random_state=2)\n",
        "svm_clf.fit(X, y)\n",
        "svm_clf.predict(np.array([[5, 2], [4, 1]]))"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.],\n",
              "       [0.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nzk1MOhVRj87",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 290
        },
        "outputId": "a1d9b378-ca5d-47d2-b0df-d6b0b8f1ff18"
      },
      "source": [
        "plt.plot(range(svm_clf.n_epochs), svm_clf.Js)\n",
        "plt.axis([0, svm_clf.n_epochs, 0, 100])"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 60000.0, 0.0, 100.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEACAYAAABPiSrXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAYBElEQVR4nO3df5TddX3n8ed7ZpKZJJOBxPw0aAIpEDdYomTxR4vSIl1+aOWY7h6Eurptjcqy7qnHU7ELloIUaPdYT6Xq5iz+qIGq7QG0lWWtFq1QdA0KlNRIifyGQALkdzLJzHz2j/u9w53LhHzJvXfu5848H+fMyb2f74/P+zP33ry+v+53IqWEJElldLW7AElS5zA0JEmlGRqSpNIMDUlSaYaGJKk0Q0OSVJqhIUkqrVRoRMTFEbEhIgYj4kt1086IiE0RsTcibo+IpTXTeiPiCxGxMyK2RMRHmly/JGkCld3TeBL4JPCF2saImAfcBFwGzAU2AF+rmeVy4HhgKfBrwB9ExFmNlSxJapd4Od8Ij4hPAseklN5XPF8LvC+l9Obi+SxgG/C6lNKmiHiymP7tYvqVwPEppfObOwxJ0kToaXD5lcC91ScppT0RsRlYGRFPA4trpxePzxtvRUUArQXomjFwSs9RC8ZMf+2SoxosVZImt7vvvntbSml+K/toNDT6ga11bTuA2cW06vP6aS+SUloHrAPoXXx8WvzeT4+ZvuGacxssVZImt4h4pNV9NHr11G5goK5tANhVTKNuenVaKYuP6muoOElSczUaGhuBk6tPinMay4GNKaXngadqpxePN5ZdeTRYnCSpucpectsTEX1AN9AdEX0R0QPcDJwUEWuK6Z8A7kspbSoW/Svg0oiYExErgPcDXypb3IVvXHr4mSRJE6bsnsalwD7gEuC3i8eXppS2AmuAq4DngTcAtVdG/RGwGXgE+D7wZyml28oWd8ycGWVnlSRNgFInwlNKl1P5zsV4074DrDjEtEHgd4ofSVKH8zYikqTSDA1JUmlZh8ar5s4EYF7/9DZXIkmCzEPjlxZUvh/4gbcsb3MlkiTIPDSqwi9sSFIWsg4Ns0KS8pJ1aEiS8tIRofEy7t4uSWqhrEMjPJkhSVnJOjQkSXnpiNBIeHxKknKQdWh4cEqS8pJ1aEiS8tIRoeHVU5KUh6xDw4unJCkvWYeGJCkvHREaHp2SpDxkHRrh9VOSlJWsQ0OSlJeOCA2vnpKkPGQdGl49JUl5yTo0JEl56YjQ8N5TkpSHjggNSVIeDA1JUmkdERpePSVJecg6NLx6SpLyknVoSJLyYmhIkkrLOjS895Qk5SXr0JAk5aUjQiN5+ZQkZSHr0PDqKUnKS9ahIUnKS8OhERHLIuLWiHg+IrZExHUR0VNMWxURd0fE3uLfVUfSh0enJCkPzdjT+CzwDLAYWAW8FbgoIqYD3wDWA3OALwPfKNpL8eiUJOWlGaFxLPD1lNL+lNIW4DZgJXA60AN8OqU0mFL6Cyo58OtN6FOS1AbNCI1PA+dHxMyIWAKczQvBcV8ae+nTfUX7i0TE2ojYEBEb6qd5dEqS8tCM0PgnKkGwE3gc2ADcAvQDO+rm3QHMHm8lKaV1KaXVKaXV1bbw8ilJykpDoRERXVT2Km4CZgHzqJy/uBbYDQzULTIA7GqkT0lS+zS6pzEXeDVwXXHe4lngi8A5wEbgl2Ps7sIvF+0vi1dPSVIeGgqNlNI24CHgQxHRExFHA++lcu7ie8Aw8OGI6I2Ii4vF/rHs+j04JUl5acY5jXcBZwFbgQeBg8Dvp5QOAOcB/xnYDvwOcF7RLknqQD2NriCldA+Vy2vHm/ZT4JSG+/D6KUnKQta3EfHiKUnKS9ahIUnKS0eEhldPSVIesg4Nv9wnSXnJOjQkSXnpiNDw6JQk5aEjQkOSlAdDQ5JUWmeEhpdPSVIWsg8NL6CSpHxkHxqSpHx0RGh4cEqS8pB9aHh0SpLykX1oSJLy0RGh4cVTkpSH7EPD+09JUj6yDw1JUj46IjT8y32SlIfsQ8ODU5KUj2xDY8Wi2e0uQZJUJ9vQ6Ko5Ae7VU5KUh2xDo8qLpyQpH9mHhiQpHx0RGh6dkqQ8ZBsaZ7xmAQDh9VOSlI1sQ2Nad7alSdKU1RH/M3v1lCTlIf/Q8OiUJGUj/9CQJGWjI0LDe09JUh6yDw2PTklSPrIPDcAvakhSJrIPDW8jIkn5aFpoRMT5EfGziNgTEZsj4rSi/YyI2BQReyPi9ohYWmZ97z711c0qTZLUJE0JjYg4E7gW+C/AbOAtwC8iYh5wE3AZMBfYAHytzDpn9/WMPvbolCTloefws5Tyx8AVKaUfFs+fAIiItcDGlNLfFM8vB7ZFxIqU0qYyK/Y2IpKUj4b3NCKiG1gNzI+IByPi8Yi4LiJmACuBe6vzppT2AJuL9vr1rI2IDRGxodGaJEmt0YzDUwuBacBvAacBq4DXAZcC/cCOuvl3UDmENUZKaV1KaXVKafU405pQpiSpUc0IjX3Fv59JKT2VUtoGfAo4B9gNDNTNPwDsKrtyr56SpHw0HBoppeeBxxl7vrr6eCNwcrUxImYBy4t2SVKHadYlt18E/ltELIiIOcDvA38P3AycFBFrIqIP+ARwX9mT4FUenZKkPDQrNK4Efgw8APwM+ClwVUppK7AGuAp4HngDcP7LWbFHpyQpH00JjZTSwZTSRSmlo1NKi1JKH04p7S+mfSeltCKlNCOldHpK6eGXs+49B4b533c81IwyJUkNyv42IpKkfBgakqTSDA1JUmmGhiSptI4Jjf0Hh9tdgiRNeR0TGv/1hp+0uwRJmvI6JjS+u+mZdpcgSVNex4SGJKn9sg2N8W5UeHB4ZOILkSSNyjY0enu6AZg/u3e0bdNTpW+OK0lqgWxDo+rWD582+vgd193RxkokSVmGxqKBvtHH8/qnt7ESSVKtLEOj9pBU1J3cGBnxPumS1C5ZhsZL+fa/bml3CZI0ZXVcaHxwvV/yk6R26YjQuPH9b2h3CZIkOiQ03rx83pjnw57XkKS26IjQqLf8D29tdwmSNCV1TGis/10PUUlSu3VMaPzq8WMPUXmrdEmaeB0TGvVWXHZbu0uQpCmnY0NDkjTxOio0fv7Js9pdgiRNaR0VGtU730qS2qOjQgPgrJWL2l2CJE1ZHRcan3/PKaOPl13yrTZWIklTT8eFhiSpfToyNB6+5tzRx489t7eNlUjS1NKRoQHQ3VX5Oxun/entba5EkqaOjg2NzX9yzujjP7z5X9pYiSRNHR0bGgB//JsrAbjxR4/6F/0kaQJ0dGi8983LRh8f551vJanlOjo0AB66+oXDVG/71PfbWIkkTX4dHxoRwd9+8E0APPjMbv7hX59uc0WSNHk1LTQi4viI2B8R62vaLoiIRyJiT0TcEhFzm9VfrdXL5vKOk18JwPv/agNPbt/Xim4kacpr5p7GXwI/rj6JiJXA/wLeAywE9gKfbWJ/Y3zm3a8bffzma/6RZ3btb1VXkjRlNSU0IuJ8YDvw3ZrmC4G/Syn9U0ppN3AZ8K6ImN2MPsdT+6W/U6/6rsEhSU3WcGhExABwBfCRukkrgXurT1JKm4EDwAmHWM/aiNgQERu2bt16xPXUB4ffGJek5mnGnsaVwPUppcfr2vuBHXVtO4Bx9zRSSutSSqtTSqvnz5/fUEG1wXHan97Oe67/UUPrkyRVNBQaEbEKeBvw5+NM3g0M1LUNALsa6bOsh685l6NnTgPgB/+2zTviSlITNLqncTqwDHg0IrYAHwXWRMRPgI3AydUZI+I4oBd4oME+S7vnE7/BRacvH32+7JJvcf8T9Ts/kqSyIqUjv/1GRMxk7N7ER6mEyIeABcBdwLnAT6hcSdWTUjr/cOtdvXp12rBhwxHXVe+5PQd4/ZX/MKbtoavPISKa1ocktVtE3J1SWt3KPhra00gp7U0pban+UDkktT+ltDWltBH4IHAD8AyVcxkXNVzxEZg7a/qY8xwAx378Vo77uIesJOnlaGhPo1WavadRa//BYVZcdtuYtiVHz+DOS369Jf1J0kTJfk+jE/VN6+bha87l87/9wp+NfWL7PpZd8i1PlkvSYUy5PY1637z3ST781z99UfslZ6/gg29dPs4SkpSnidjTmPKhUfXYc3sP+VcAz1ixgOvf9+8ntB5JerkMjTZIKXHsx1/6b3P8v/9xBgtm901QRZJUjqHRZjv2HuTkK7592Pl+8Ae/xqvmzpyAiiTp0AyNjAwODXPipbcdfsbC1z/wJlYvncPzew8wd9Z0vxMiqeUMjYzd/8QO3v6ZOxpax+cufD1nnbTIQJHUFIZGB9k9OMRJf/R/m7rO1y45iivPO4nXLJ5Nb093U9ctafIxNDpcSokbfvQol95yf0vWv2LRbD529gp+aX4/r+ifzszpPS3pR1JnMDQmsZQS37z3Sf77V+9p6npXvnKAWdN7mNnbzey+yl1++3t7mDGtm+k9XTy9cz8PPL2LjU/uHF3mY2et4LVLjqJvWhe9Pd0Mp8QX73yIExbOZvn8fl41dwZLjp7BQN80IvBwmpSpiQgNN03bJCJ456olvHPVkpecL6XEL7bt4Yt3PsT6Hz562PV2RdDVBU/vHOTfnt5NVxfs3j/EnsFhhkZGGBlnG+Ha2zYd6TDa6sx/t5D7n9jBiYtms/ioGTzw9C4WH9XHq+bO5L7Ht9PT1cWcmdM4cdEAPV3B3gPD7D0wxPzZvUQE+w8O0zetm6HhEXbtH+L2nz/Dxid38qbjXsFdv3gWgJOWDHD/Ey8E7Lz+XlYsms2s3m5WL53L9n0HmDNzOnsGhwHom9ZFd1clVHfsO8gzOwcZSYkTF439MzKDQyNs2bGfY+bM4PsPbGXB7F72Hhjm1GPnjpkvIkgp0RXByDgbeNXp2/ceZM6s6QSQgANDI9z1i2d543Fz6e3p5it3PcyJi2Zz6rGvGF32rs3bePjZvbz71Fdz9yPP0Tetm5WvPIp7H9vO4qP7mN/fO7qBMDg0zI69B1kw0DfaB8DB4REODI0wq7eHroCUYOf+g0zr7mLGtG6uv+MhXr90DqtedTTjbWpEscyhNl237R5k8OAIx8yZMaZ938FhHntuLycsfOH3Wt2WGR5JPPzsHo6d108U7dWah0cSew8M09/74v/6qrWMt01UXX5waISerhh9jSdKtbf631MAu/YPsefAMAsHeiemFvc0ppaDwyPsGRxi2+5BtuwY5Kkd+1hy9Ax6ursYHBpm8OAID27dzTX/pzODRJrKHrn27R6e0tRT/56sbv3Vb5GmlMY8r26JBy9slVeXGym21odH0uiWZHV91S35oeFEIjGtu4uh4RfWXO1lWncXB4ZG6O4O0ghEF2P2AGrrLDvO6p5CRDAykugabwu2dn1R08dh+hlOie5isIlEjLOtX/291M4zNDJCT9eLb0vX3R0MDY8UZcTo8vVb5iMJumq2+nu6uqh9pYIg1RV/qEOewyNpdF219Q+Pvta166j8W329q3sDta9Hdbz1exXVecq8frW/szLzH2qeVFP/4eapTopxpsELr/Xc/l4PT2nqqf8PpPr0xf+vTPy5lVkTcwRAytaUu8utJOnIGRqSpNIMDUlSaYaGJKk0Q0OSVJqhIUkqzdCQJJVmaEiSSjM0JEmlGRqSpNIMDUlSaYaGJKk0Q0OSVJqhIUkqzdCQJJVmaEiSSjM0JEmlGRqSpNIMDUlSaQ2HRkT0RsT1EfFIROyKiHsi4uya6WdExKaI2BsRt0fE0kb7lCS1RzP2NHqAx4C3AkcBlwJfj4hlETEPuAm4DJgLbAC+1oQ+JUlt0NPoClJKe4DLa5r+PiIeAk4BXgFsTCn9DUBEXA5si4gVKaVNjfYtSZpYTT+nERELgROAjcBK4N7qtCJgNhft9cutjYgNEbFh69atzS5LktQETQ2NiJgG3AB8udiT6Ad21M22A5hdv2xKaV1KaXVKafX8+fObWZYkqUmaFhoR0QV8BTgAXFw07wYG6mYdAHY1q19J0sRpSmhERADXAwuBNSmlg8WkjcDJNfPNApYX7ZKkDtOsPY3PAa8B3pFS2lfTfjNwUkSsiYg+4BPAfZ4El6TO1IzvaSwFPgCsArZExO7i58KU0lZgDXAV8DzwBuD8RvuUJLVHMy65fQSIl5j+HWBFo/1IktrP24hIkkozNCRJpRkakqTSDA1JUmmGhiSpNENDklSaoSFJKs3QkCSVZmhIkkozNCRJpRkakqTSDA1JUmmGhiSpNENDklSaoSFJKs3QkCSVZmhIkkozNCRJpRkakqTSDA1JUmmGhiSpNENDklSaoSFJKs3QkCSVZmhIkkozNCRJpRkakqTSDA1JUmmGhiSpNENDklSaoSFJKs3QkCSVZmhIkkozNCRJpbU8NCJibkTcHBF7IuKRiLig1X1KklqjZwL6+EvgALAQWAV8KyLuTSltnIC+JUlN1NI9jYiYBawBLksp7U4p3QF8E3hPK/uVJLVGq/c0TgCGUkoP1LTdC7y1fsaIWAusLZ4ORsT9La6tneYB29pdRItM5rGB4+t0k318J7a6g1aHRj+ws65tBzC7fsaU0jpgHUBEbEgprW5xbW0zmcc3mccGjq/TTYXxtbqPVp8I3w0M1LUNALta3K8kqQVaHRoPAD0RcXxN28mAJ8ElqQO1NDRSSnuAm4ArImJWRPwK8E7gK4dZdF0r68rAZB7fZB4bOL5O5/gaFCml1nYQMRf4AnAm8CxwSUrpxpZ2KklqiZaHhiRp8vA2IpKk0gwNSVJpWYVG7vepioiLI2JDRAxGxJfqpp0REZsiYm9E3B4RS2um9UbEFyJiZ0RsiYiPNGvZJo6tNyKuL37vuyLinog4e7KMr+hrfUQ8VfT1QET83mQaX02fx0fE/ohYX9N2QfHa7omIW4pzjdVpL/m5a2TZJo/re8W4dhc/P59M4yv6Oz8iflb0tzkiTiva83l/ppSy+QH+GvgalS8F/iqVLwKubHddNfW9CzgP+BzwpZr2eUWt/xHoA/4M+GHN9KuBHwBzgNcAW4CzGl22yWObBVwOLKOyMfF2Kt+nWTYZxlf0tRLoLR6vKPo6ZbKMr6bPbxd9rq8Z9y7gLcVn60bgq2U+d40s24JxfQ/4vUO8rpNhfGcCjwBvpPIZXFL8ZPX+bNkb9wh+YbOo3NjwhJq2rwDXtLu2cWr9JGNDYy3wz3Vj2QesKJ4/CfxGzfQrq2/MRpadgHHeR+XeYZNufFRut/AU8J8m0/iA84GvU9kAqIbGnwA31syzvPiszT7c566RZVswtu8xfmhMlvH9M/C747Rn9f7M6fDUoe5TtbJN9bwcK6nUCox+P2UzsDIi5gCLa6czdlyNLNsyEbGQymuyscEasxpfRHw2IvYCm6iExq0N1pjN+CJiALgCqD/EUF/jZor/DDn8566RZVvh6ojYFhF3RsTpTagxi/FFRDewGpgfEQ9GxOMRcV1EzBinxra+P3MKjdL3qcpQP5Vaa1Vr7695Xj+t0WVbIiKmATcAX04pbWqwxqzGl1K6qFj/aVS+eDrYYI05je9K4PqU0uN17Yer8aU+d40s22wfA46jcshmHfB3EbG8wRpzGd9CYBrwW1Tem6uA1wGXlqgRJvD9mVNodPJ9ql6q9t01z+unNbps00VEF5Vd8APAxU2oMavxAaSUhlPlNv3HAB9qsMYsxhcRq4C3AX8+zuTD1fhSn7tGlm2qlNKPUkq7UkqDKaUvA3cC5zRYYy7j21f8+5mU0lMppW3Apyg3PpjA92dOodHJ96naSKVWYPTviCwHNqaUnqdyGOTkmvlrx9XIsk0VEQFcT2WrZ01K6WATasxmfOPoqdbSQI25jO90KhctPBoRW4CPAmsi4ifj1Hgc0EvlM3e4z10jy7ZaAqLBGrMYX/FeeZzKmEabD1Fje9+frTih08CJoK9SuVphFvAr5Hf1VA+VKxCuprI13le0zS9qXVO0XcvYKxSuAb5P5QqFFcULVb264YiXbcH4Pg/8EOiva+/48QELqJwk7ge6gf8A7AF+c5KMbyawqObnfwJ/W9S3ksphltOKz9Z6xl4hdMjPXSPLNnl8RxevWfUzd2Hx+p0wGcZX9HUF8OPivTqHylVNV+b2/mz6wBv8pc0FbineDI8CF7S7prr6LqeS/rU/lxfT3kbl5Oo+Kld5LKtZrpfK/bd2Ak8DH6lb7xEv28SxLS3Gs5/Kbmv158JJMr75xYdje9HXvwDvb0aNOYzvEO/V9TXPLyg+U3uAbwBza6a95OeukWWb/Pr9mMqhk+1UNm7OnCzjK/qaBny2GN8W4C+Avtzen957SpJUWk7nNCRJmTM0JEmlGRqSpNIMDUlSaYaGJKk0Q0OSVJqhIUkqzdCQJJX2/wEGW4aqH2501gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IgmyKxEARj89",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "b712d5cd-8e73-4d8b-c849-26c92a006318"
      },
      "source": [
        "print(svm_clf.intercept_, svm_clf.coef_)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-15.56761653] [[[2.28120287]\n",
            "  [2.71621742]]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v5k35cBZRj9A",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5a24aedf-59f6-49d8-df79-0fc6b250a5c2"
      },
      "source": [
        "svm_clf2 = SVC(kernel=\"linear\", C=C)\n",
        "svm_clf2.fit(X, y.ravel())\n",
        "print(svm_clf2.intercept_, svm_clf2.coef_)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-15.51721253] [[2.27128546 2.71287145]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ayJHbF_Rj9C",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 277
        },
        "outputId": "4656badf-40bb-435a-f8d6-9d5eed418571"
      },
      "source": [
        "yr = y.ravel()\n",
        "plt.figure(figsize=(12,3.2))\n",
        "plt.subplot(121)\n",
        "plt.plot(X[:, 0][yr==1], X[:, 1][yr==1], \"g^\", label=\"Iris-Virginica\")\n",
        "plt.plot(X[:, 0][yr==0], X[:, 1][yr==0], \"bs\", label=\"Not Iris-Virginica\")\n",
        "plot_svc_decision_boundary(svm_clf, 4, 6)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.title(\"MyLinearSVC\", fontsize=14)\n",
        "plt.axis([4, 6, 0.8, 2.8])\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.plot(X[:, 0][yr==1], X[:, 1][yr==1], \"g^\")\n",
        "plt.plot(X[:, 0][yr==0], X[:, 1][yr==0], \"bs\")\n",
        "plot_svc_decision_boundary(svm_clf2, 4, 6)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.title(\"SVC\", fontsize=14)\n",
        "plt.axis([4, 6, 0.8, 2.8])\n"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4.0, 6.0, 0.8, 2.8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x230.4 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "g-OAiFoMRj9F",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "f8861196-b944-4d51-8c29-acb2c03539ae"
      },
      "source": [
        "from sklearn.linear_model import SGDClassifier\n",
        "\n",
        "sgd_clf = SGDClassifier(loss=\"hinge\", alpha = 0.017, max_iter = 50, tol=-np.infty, random_state=42)\n",
        "sgd_clf.fit(X, y.ravel())\n",
        "\n",
        "m = len(X)\n",
        "t = y * 2 - 1  # -1 if t==0, +1 if t==1\n",
        "X_b = np.c_[np.ones((m, 1)), X]  # Add bias input x0=1\n",
        "X_b_t = X_b * t\n",
        "sgd_theta = np.r_[sgd_clf.intercept_[0], sgd_clf.coef_[0]]\n",
        "print(sgd_theta)\n",
        "support_vectors_idx = (X_b_t.dot(sgd_theta) < 1).ravel()\n",
        "sgd_clf.support_vectors_ = X[support_vectors_idx]\n",
        "sgd_clf.C = C\n",
        "\n",
        "plt.figure(figsize=(5.5,3.2))\n",
        "plt.plot(X[:, 0][yr==1], X[:, 1][yr==1], \"g^\")\n",
        "plt.plot(X[:, 0][yr==0], X[:, 1][yr==0], \"bs\")\n",
        "plot_svc_decision_boundary(sgd_clf, 4, 6)\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.title(\"SGDClassifier\", fontsize=14)\n",
        "plt.axis([4, 6, 0.8, 2.8])\n"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-12.46916922   1.96411117   1.74274779]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4.0, 6.0, 0.8, 2.8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 396x230.4 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ujmnKgWARj9H",
        "colab_type": "text"
      },
      "source": [
        "# Exercise solutions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o4Oslg8URj9I",
        "colab_type": "text"
      },
      "source": [
        "## 1. to 7."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "p9X4DIdDRj9I",
        "colab_type": "text"
      },
      "source": [
        "See appendix A."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3VaHLRUNRj9J",
        "colab_type": "text"
      },
      "source": [
        "# 8."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2YFrzzkvRj9J",
        "colab_type": "text"
      },
      "source": [
        "_Exercise: train a `LinearSVC` on a linearly separable dataset. Then train an `SVC` and a `SGDClassifier` on the same dataset. See if you can get them to produce roughly the same model._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qNmjthTKRj9J",
        "colab_type": "text"
      },
      "source": [
        "Let's use the Iris dataset: the Iris Setosa and Iris Versicolor classes are linearly separable."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sv_rla1aRj9K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn import datasets\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
        "y = iris[\"target\"]\n",
        "\n",
        "setosa_or_versicolor = (y == 0) | (y == 1)\n",
        "X = X[setosa_or_versicolor]\n",
        "y = y[setosa_or_versicolor]"
      ],
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g2l4H_uIRj9L",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "166593d9-3973-4373-cee0-3be3d610ded9"
      },
      "source": [
        "from sklearn.svm import SVC, LinearSVC\n",
        "from sklearn.linear_model import SGDClassifier\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "C = 5\n",
        "alpha = 1 / (C * len(X))\n",
        "\n",
        "lin_clf = LinearSVC(loss=\"hinge\", C=C, random_state=42)\n",
        "svm_clf = SVC(kernel=\"linear\", C=C)\n",
        "sgd_clf = SGDClassifier(loss=\"hinge\", learning_rate=\"constant\", eta0=0.001, alpha=alpha,\n",
        "                        max_iter=100000, tol=-np.infty, random_state=42)\n",
        "\n",
        "scaler = StandardScaler()\n",
        "X_scaled = scaler.fit_transform(X)\n",
        "\n",
        "lin_clf.fit(X_scaled, y)\n",
        "svm_clf.fit(X_scaled, y)\n",
        "sgd_clf.fit(X_scaled, y)\n",
        "\n",
        "print(\"LinearSVC:                   \", lin_clf.intercept_, lin_clf.coef_)\n",
        "print(\"SVC:                         \", svm_clf.intercept_, svm_clf.coef_)\n",
        "print(\"SGDClassifier(alpha={:.5f}):\".format(sgd_clf.alpha), sgd_clf.intercept_, sgd_clf.coef_)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LinearSVC:                    [0.28474272] [[1.05364736 1.09903308]]\n",
            "SVC:                          [0.31896852] [[1.1203284  1.02625193]]\n",
            "SGDClassifier(alpha=0.00200): [0.319] [[1.12087283 1.02679408]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qnwXb1lORj9N",
        "colab_type": "text"
      },
      "source": [
        "Let's plot the decision boundaries of these three models:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6WKoOZn7Rj9O",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "889a3330-efcf-478f-cfa9-41383b210821"
      },
      "source": [
        "# Compute the slope and bias of each decision boundary\n",
        "w1 = -lin_clf.coef_[0, 0]/lin_clf.coef_[0, 1]\n",
        "b1 = -lin_clf.intercept_[0]/lin_clf.coef_[0, 1]\n",
        "w2 = -svm_clf.coef_[0, 0]/svm_clf.coef_[0, 1]\n",
        "b2 = -svm_clf.intercept_[0]/svm_clf.coef_[0, 1]\n",
        "w3 = -sgd_clf.coef_[0, 0]/sgd_clf.coef_[0, 1]\n",
        "b3 = -sgd_clf.intercept_[0]/sgd_clf.coef_[0, 1]\n",
        "\n",
        "# Transform the decision boundary lines back to the original scale\n",
        "line1 = scaler.inverse_transform([[-10, -10 * w1 + b1], [10, 10 * w1 + b1]])\n",
        "line2 = scaler.inverse_transform([[-10, -10 * w2 + b2], [10, 10 * w2 + b2]])\n",
        "line3 = scaler.inverse_transform([[-10, -10 * w3 + b3], [10, 10 * w3 + b3]])\n",
        "\n",
        "# Plot all three decision boundaries\n",
        "plt.figure(figsize=(11, 4))\n",
        "plt.plot(line1[:, 0], line1[:, 1], \"k:\", label=\"LinearSVC\")\n",
        "plt.plot(line2[:, 0], line2[:, 1], \"b--\", linewidth=2, label=\"SVC\")\n",
        "plt.plot(line3[:, 0], line3[:, 1], \"r-\", label=\"SGDClassifier\")\n",
        "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\") # label=\"Iris-Versicolor\"\n",
        "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\") # label=\"Iris-Setosa\"\n",
        "plt.xlabel(\"Petal length\", fontsize=14)\n",
        "plt.ylabel(\"Petal width\", fontsize=14)\n",
        "plt.legend(loc=\"upper center\", fontsize=14)\n",
        "plt.axis([0, 5.5, 0, 2])\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ABWyPPIvRj9Q",
        "colab_type": "text"
      },
      "source": [
        "Close enough!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nRSBslZYRj9R",
        "colab_type": "text"
      },
      "source": [
        "# 9."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zgbpRFIsRj9R",
        "colab_type": "text"
      },
      "source": [
        "_Exercise: train an SVM classifier on the MNIST dataset. Since SVM classifiers are binary classifiers, you will need to use one-versus-all to classify all 10 digits. You may want to tune the hyperparameters using small validation sets to speed up the process. What accuracy can you reach?_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6A2oIFR1Rj9S",
        "colab_type": "text"
      },
      "source": [
        "First, let's load the dataset and split it into a training set and a test set. We could use `train_test_split()` but people usually just take the first 60,000 instances for the training set, and the last 10,000 instances for the test set (this makes it possible to compare your model's performance with others): "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EUm8hIfQRj9S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "try:\n",
        "    from sklearn.datasets import fetch_openml\n",
        "    mnist = fetch_openml('mnist_784', version=1, cache=True)\n",
        "except ImportError:\n",
        "    from sklearn.datasets import fetch_mldata\n",
        "    mnist = fetch_mldata('MNIST original')\n",
        "\n",
        "X = mnist[\"data\"]\n",
        "y = mnist[\"target\"]\n",
        "\n",
        "X_train = X[:60000]\n",
        "y_train = y[:60000]\n",
        "X_test = X[60000:]\n",
        "y_test = y[60000:]"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZNqlW2OsRj9V",
        "colab_type": "text"
      },
      "source": [
        "Many training algorithms are sensitive to the order of the training instances, so it's generally good practice to shuffle them first:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bYthcv-rRj9V",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(42)\n",
        "rnd_idx = np.random.permutation(60000)\n",
        "X_train = X_train[rnd_idx]\n",
        "y_train = y_train[rnd_idx]"
      ],
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jq410fXcRj9X",
        "colab_type": "text"
      },
      "source": [
        "Let's start simple, with a linear SVM classifier. It will automatically use the One-vs-All (also called One-vs-the-Rest, OvR) strategy, so there's nothing special we need to do. Easy!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-refWTSYRj9X",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "208230eb-bb4a-43d6-ad81-33d4e02a84df"
      },
      "source": [
        "lin_clf = LinearSVC(random_state=42)\n",
        "lin_clf.fit(X_train, y_train)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
              "          intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
              "          multi_class='ovr', penalty='l2', random_state=42, tol=0.0001,\n",
              "          verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Uc5yuhtfRj9b",
        "colab_type": "text"
      },
      "source": [
        "Let's make predictions on the training set and measure the accuracy (we don't want to measure it on the test set yet, since we have not selected and trained the final model yet):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nn4GWfvjRj9b",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "30165e54-0f52-446f-916e-125e38424db0"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "y_pred = lin_clf.predict(X_train)\n",
        "accuracy_score(y_train, y_pred)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8946"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2r1RLOkrRj9f",
        "colab_type": "text"
      },
      "source": [
        "Wow, 86% accuracy on MNIST is a really bad performance. This linear model is certainly too simple for MNIST, but perhaps we just needed to scale the data first:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OFRbB3mIRj9f",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "scaler = StandardScaler()\n",
        "X_train_scaled = scaler.fit_transform(X_train.astype(np.float32))\n",
        "X_test_scaled = scaler.transform(X_test.astype(np.float32))"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mAAUugxmRj9h",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "43637696-10c5-4647-dd25-73fb1c767bd9"
      },
      "source": [
        "lin_clf = LinearSVC(random_state=42)\n",
        "lin_clf.fit(X_train_scaled, y_train)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
              "          intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
              "          multi_class='ovr', penalty='l2', random_state=42, tol=0.0001,\n",
              "          verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gAyOnprZRj9j",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "9c1a667c-44af-4539-e30b-abeec6db2dcc"
      },
      "source": [
        "y_pred = lin_clf.predict(X_train_scaled)\n",
        "accuracy_score(y_train, y_pred)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9215166666666667"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AlI4LqExRj9m",
        "colab_type": "text"
      },
      "source": [
        "That's much better (we cut the error rate in two), but still not great at all for MNIST. If we want to use an SVM, we will have to use a kernel. Let's try an `SVC` with an RBF kernel (the default).\n",
        "\n",
        "**Warning**: if you are using Scikit-Learn ≤ 0.19, the `SVC` class will use the One-vs-One (OvO) strategy by default, so you must explicitly set `decision_function_shape=\"ovr\"` if you want to use the OvR strategy instead (OvR is the default since 0.19)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bVWFFGHpRj9m",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "d99ddade-5a0c-4f8d-eeeb-d772e0c8f16a"
      },
      "source": [
        "svm_clf = SVC(decision_function_shape=\"ovr\", gamma=\"auto\")\n",
        "svm_clf.fit(X_train_scaled[:10000], y_train[:10000])"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=1.0, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
              "    decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',\n",
              "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
              "    tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UkyMFWejRj9o",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6dbf2d7b-159a-4be1-f4f1-db5351a9ed30"
      },
      "source": [
        "y_pred = svm_clf.predict(X_train_scaled)\n",
        "accuracy_score(y_train, y_pred)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9476"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SSwnJAIyRj9q",
        "colab_type": "text"
      },
      "source": [
        "That's promising, we get better performance even though we trained the model on 6 times less data. Let's tune the hyperparameters by doing a randomized search with cross validation. We will do this on a small dataset just to speed up the process:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "al5ls9KbRj9r",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "41ff89ec-29b3-4902-ab11-37c1f1745872"
      },
      "source": [
        "from sklearn.model_selection import RandomizedSearchCV\n",
        "from scipy.stats import reciprocal, uniform\n",
        "\n",
        "param_distributions = {\"gamma\": reciprocal(0.001, 0.1), \"C\": uniform(1, 10)}\n",
        "rnd_search_cv = RandomizedSearchCV(svm_clf, param_distributions, n_iter=10, verbose=2, cv=3)\n",
        "rnd_search_cv.fit(X_train_scaled[:1000], y_train[:1000])"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting 3 folds for each of 10 candidates, totalling 30 fits\n",
            "[CV] C=8.852316058423087, gamma=0.001766074650481071 .................\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[CV] .. C=8.852316058423087, gamma=0.001766074650481071, total=   1.1s\n",
            "[CV] C=8.852316058423087, gamma=0.001766074650481071 .................\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    1.1s remaining:    0.0s\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[CV] .. C=8.852316058423087, gamma=0.001766074650481071, total=   1.0s\n",
            "[CV] C=8.852316058423087, gamma=0.001766074650481071 .................\n",
            "[CV] .. C=8.852316058423087, gamma=0.001766074650481071, total=   1.1s\n",
            "[CV] C=1.8271960104746645, gamma=0.006364737055453384 ................\n",
            "[CV] . C=1.8271960104746645, gamma=0.006364737055453384, total=   1.3s\n",
            "[CV] C=1.8271960104746645, gamma=0.006364737055453384 ................\n",
            "[CV] . C=1.8271960104746645, gamma=0.006364737055453384, total=   1.3s\n",
            "[CV] C=1.8271960104746645, gamma=0.006364737055453384 ................\n",
            "[CV] . C=1.8271960104746645, gamma=0.006364737055453384, total=   1.3s\n",
            "[CV] C=9.875199193765326, gamma=0.051349833451870636 .................\n",
            "[CV] .. C=9.875199193765326, gamma=0.051349833451870636, total=   1.3s\n",
            "[CV] C=9.875199193765326, gamma=0.051349833451870636 .................\n",
            "[CV] .. C=9.875199193765326, gamma=0.051349833451870636, total=   1.3s\n",
            "[CV] C=9.875199193765326, gamma=0.051349833451870636 .................\n",
            "[CV] .. C=9.875199193765326, gamma=0.051349833451870636, total=   1.3s\n",
            "[CV] C=6.59992909281409, gamma=0.05991666578466177 ...................\n",
            "[CV] .... C=6.59992909281409, gamma=0.05991666578466177, total=   1.3s\n",
            "[CV] C=6.59992909281409, gamma=0.05991666578466177 ...................\n",
            "[CV] .... C=6.59992909281409, gamma=0.05991666578466177, total=   1.3s\n",
            "[CV] C=6.59992909281409, gamma=0.05991666578466177 ...................\n",
            "[CV] .... C=6.59992909281409, gamma=0.05991666578466177, total=   1.3s\n",
            "[CV] C=9.053435975487119, gamma=0.003596490522533181 .................\n",
            "[CV] .. C=9.053435975487119, gamma=0.003596490522533181, total=   1.2s\n",
            "[CV] C=9.053435975487119, gamma=0.003596490522533181 .................\n",
            "[CV] .. C=9.053435975487119, gamma=0.003596490522533181, total=   1.2s\n",
            "[CV] C=9.053435975487119, gamma=0.003596490522533181 .................\n",
            "[CV] .. C=9.053435975487119, gamma=0.003596490522533181, total=   1.2s\n",
            "[CV] C=2.701062804458301, gamma=0.004002330992905356 .................\n",
            "[CV] .. C=2.701062804458301, gamma=0.004002330992905356, total=   1.2s\n",
            "[CV] C=2.701062804458301, gamma=0.004002330992905356 .................\n",
            "[CV] .. C=2.701062804458301, gamma=0.004002330992905356, total=   1.2s\n",
            "[CV] C=2.701062804458301, gamma=0.004002330992905356 .................\n",
            "[CV] .. C=2.701062804458301, gamma=0.004002330992905356, total=   1.2s\n",
            "[CV] C=3.2711787843881437, gamma=0.017596957507461645 ................\n",
            "[CV] . C=3.2711787843881437, gamma=0.017596957507461645, total=   1.3s\n",
            "[CV] C=3.2711787843881437, gamma=0.017596957507461645 ................\n",
            "[CV] . C=3.2711787843881437, gamma=0.017596957507461645, total=   1.3s\n",
            "[CV] C=3.2711787843881437, gamma=0.017596957507461645 ................\n",
            "[CV] . C=3.2711787843881437, gamma=0.017596957507461645, total=   1.3s\n",
            "[CV] C=6.848991127746501, gamma=0.01573529056426603 ..................\n",
            "[CV] ... C=6.848991127746501, gamma=0.01573529056426603, total=   1.3s\n",
            "[CV] C=6.848991127746501, gamma=0.01573529056426603 ..................\n",
            "[CV] ... C=6.848991127746501, gamma=0.01573529056426603, total=   1.3s\n",
            "[CV] C=6.848991127746501, gamma=0.01573529056426603 ..................\n",
            "[CV] ... C=6.848991127746501, gamma=0.01573529056426603, total=   1.3s\n",
            "[CV] C=2.893035364914488, gamma=0.03834647526105027 ..................\n",
            "[CV] ... C=2.893035364914488, gamma=0.03834647526105027, total=   1.3s\n",
            "[CV] C=2.893035364914488, gamma=0.03834647526105027 ..................\n",
            "[CV] ... C=2.893035364914488, gamma=0.03834647526105027, total=   1.3s\n",
            "[CV] C=2.893035364914488, gamma=0.03834647526105027 ..................\n",
            "[CV] ... C=2.893035364914488, gamma=0.03834647526105027, total=   1.3s\n",
            "[CV] C=5.336260835426313, gamma=0.008808538172595842 .................\n",
            "[CV] .. C=5.336260835426313, gamma=0.008808538172595842, total=   1.3s\n",
            "[CV] C=5.336260835426313, gamma=0.008808538172595842 .................\n",
            "[CV] .. C=5.336260835426313, gamma=0.008808538172595842, total=   1.3s\n",
            "[CV] C=5.336260835426313, gamma=0.008808538172595842 .................\n",
            "[CV] .. C=5.336260835426313, gamma=0.008808538172595842, total=   1.3s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Done  30 out of  30 | elapsed:   37.4s finished\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RandomizedSearchCV(cv=3, error_score=nan,\n",
              "                   estimator=SVC(C=1.0, break_ties=False, cache_size=200,\n",
              "                                 class_weight=None, coef0=0.0,\n",
              "                                 decision_function_shape='ovr', degree=3,\n",
              "                                 gamma='auto', kernel='rbf', max_iter=-1,\n",
              "                                 probability=False, random_state=None,\n",
              "                                 shrinking=True, tol=0.001, verbose=False),\n",
              "                   iid='deprecated', n_iter=10, n_jobs=None,\n",
              "                   param_distributions={'C': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fc799bd9160>,\n",
              "                                        'gamma': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fc799ae03c8>},\n",
              "                   pre_dispatch='2*n_jobs', random_state=None, refit=True,\n",
              "                   return_train_score=False, scoring=None, verbose=2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6oEigH8cRj9t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "23ce455b-3849-4c2d-bb5a-0724d5286a2b"
      },
      "source": [
        "rnd_search_cv.best_estimator_"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=8.852316058423087, break_ties=False, cache_size=200, class_weight=None,\n",
              "    coef0=0.0, decision_function_shape='ovr', degree=3,\n",
              "    gamma=0.001766074650481071, kernel='rbf', max_iter=-1, probability=False,\n",
              "    random_state=None, shrinking=True, tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UUDXb-gpRj9v",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "064ceda1-6364-4a5c-9aa4-44393ac86c2d"
      },
      "source": [
        "rnd_search_cv.best_score_"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8630037222851593"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mpR2SxZjRj9x",
        "colab_type": "text"
      },
      "source": [
        "This looks pretty low but remember we only trained the model on 1,000 instances. Let's retrain the best estimator on the whole training set (run this at night, it will take hours):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ng-9ynkRRj9y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "a3eb26a5-c589-497a-f277-281162478ee2"
      },
      "source": [
        "rnd_search_cv.best_estimator_.fit(X_train_scaled, y_train)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=8.852316058423087, break_ties=False, cache_size=200, class_weight=None,\n",
              "    coef0=0.0, decision_function_shape='ovr', degree=3,\n",
              "    gamma=0.001766074650481071, kernel='rbf', max_iter=-1, probability=False,\n",
              "    random_state=None, shrinking=True, tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t2G9hsieRj90",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "76ff6795-cf91-43a6-ce2f-ec96e50156c7"
      },
      "source": [
        "y_pred = rnd_search_cv.best_estimator_.predict(X_train_scaled)\n",
        "accuracy_score(y_train, y_pred)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.99965"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oNMSzxk2Rj91",
        "colab_type": "text"
      },
      "source": [
        "Ah, this looks good! Let's select this model. Now we can test it on the test set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xuUyK9-lRj91",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "88764d02-d668-4614-cd46-acf8a21e4b4b"
      },
      "source": [
        "y_pred = rnd_search_cv.best_estimator_.predict(X_test_scaled)\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9709"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DeDuauqvRj93",
        "colab_type": "text"
      },
      "source": [
        "Not too bad, but apparently the model is overfitting slightly. It's tempting to tweak the hyperparameters a bit more (e.g. decreasing `C` and/or `gamma`), but we would run the risk of overfitting the test set. Other people have found that the hyperparameters `C=5` and `gamma=0.005` yield even better performance (over 98% accuracy). By running the randomized search for longer and on a larger part of the training set, you may be able to find this as well."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z4K2daDrRj93",
        "colab_type": "text"
      },
      "source": [
        "## 10."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gs9e-pp_Rj94",
        "colab_type": "text"
      },
      "source": [
        "_Exercise: train an SVM regressor on the California housing dataset._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TjRmzrNIRj94",
        "colab_type": "text"
      },
      "source": [
        "Let's load the dataset using Scikit-Learn's `fetch_california_housing()` function:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4yTP1PsWRj94",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "2217e5b0-2bc9-44fe-900c-1a25e41667e1"
      },
      "source": [
        "from sklearn.datasets import fetch_california_housing\n",
        "\n",
        "housing = fetch_california_housing()\n",
        "X = housing[\"data\"]\n",
        "y = housing[\"target\"]"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading Cal. housing from https://ndownloader.figshare.com/files/5976036 to /root/scikit_learn_data\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bZzO0ZRURj96",
        "colab_type": "text"
      },
      "source": [
        "Split it into a training set and a test set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uMvernljRj96",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
      ],
      "execution_count": 74,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lgdKuh0NRj99",
        "colab_type": "text"
      },
      "source": [
        "Don't forget to scale the data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZJ-nBsbTRj99",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "scaler = StandardScaler()\n",
        "X_train_scaled = scaler.fit_transform(X_train)\n",
        "X_test_scaled = scaler.transform(X_test)"
      ],
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tbb5yHMTRj-B",
        "colab_type": "text"
      },
      "source": [
        "Let's train a simple `LinearSVR` first:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KzOjhVpDRj-B",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "b9b3c880-9aa2-4c63-fd96-8342e5a4ac89"
      },
      "source": [
        "from sklearn.svm import LinearSVR\n",
        "\n",
        "lin_svr = LinearSVR(random_state=42)\n",
        "lin_svr.fit(X_train_scaled, y_train)"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearSVR(C=1.0, dual=True, epsilon=0.0, fit_intercept=True,\n",
              "          intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,\n",
              "          random_state=42, tol=0.0001, verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gstt0GGWRj-D",
        "colab_type": "text"
      },
      "source": [
        "Let's see how it performs on the training set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7yfJ75BoRj-D",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6aef7d5a-7c64-435b-ac7e-264501aa35dc"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "y_pred = lin_svr.predict(X_train_scaled)\n",
        "mse = mean_squared_error(y_train, y_pred)\n",
        "mse"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.949968822217229"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bjp8biQhRj-F",
        "colab_type": "text"
      },
      "source": [
        "Let's look at the RMSE:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pb6ht2peRj-F",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "252443f0-cf2d-4f01-a916-12b06c5c2f58"
      },
      "source": [
        "np.sqrt(mse)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9746634404845752"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sbat9--NRj-H",
        "colab_type": "text"
      },
      "source": [
        "In this training set, the targets are tens of thousands of dollars. The RMSE gives a rough idea of the kind of error you should expect (with a higher weight for large errors): so with this model we can expect errors somewhere around $10,000. Not great. Let's see if we can do better with an RBF Kernel. We will use randomized search with cross validation to find the appropriate hyperparameter values for `C` and `gamma`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ssMnccvERj-H",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "781ae6a1-4a76-4672-8068-00ab18f3318f"
      },
      "source": [
        "from sklearn.svm import SVR\n",
        "from sklearn.model_selection import RandomizedSearchCV\n",
        "from scipy.stats import reciprocal, uniform\n",
        "\n",
        "param_distributions = {\"gamma\": reciprocal(0.001, 0.1), \"C\": uniform(1, 10)}\n",
        "rnd_search_cv = RandomizedSearchCV(SVR(), param_distributions, n_iter=10, verbose=2, cv=3, random_state=42)\n",
        "rnd_search_cv.fit(X_train_scaled, y_train)"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Fitting 3 folds for each of 10 candidates, totalling 30 fits\n",
            "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n",
            "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  10.4s\n",
            "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:   10.4s remaining:    0.0s\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  10.3s\n",
            "[CV] C=4.745401188473625, gamma=0.07969454818643928 ..................\n",
            "[CV] ... C=4.745401188473625, gamma=0.07969454818643928, total=  10.4s\n",
            "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
            "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=   9.7s\n",
            "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
            "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=   9.4s\n",
            "[CV] C=8.31993941811405, gamma=0.015751320499779724 ..................\n",
            "[CV] ... C=8.31993941811405, gamma=0.015751320499779724, total=   9.6s\n",
            "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
            "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=   8.7s\n",
            "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
            "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=   8.7s\n",
            "[CV] C=2.560186404424365, gamma=0.002051110418843397 .................\n",
            "[CV] .. C=2.560186404424365, gamma=0.002051110418843397, total=   8.8s\n",
            "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
            "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=   8.8s\n",
            "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
            "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=   8.7s\n",
            "[CV] C=1.5808361216819946, gamma=0.05399484409787431 .................\n",
            "[CV] .. C=1.5808361216819946, gamma=0.05399484409787431, total=   8.8s\n",
            "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
            "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=   9.6s\n",
            "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
            "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=   9.7s\n",
            "[CV] C=7.011150117432088, gamma=0.026070247583707663 .................\n",
            "[CV] .. C=7.011150117432088, gamma=0.026070247583707663, total=  11.5s\n",
            "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
            "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=   8.6s\n",
            "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
            "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=   8.7s\n",
            "[CV] C=1.2058449429580245, gamma=0.0870602087830485 ..................\n",
            "[CV] ... C=1.2058449429580245, gamma=0.0870602087830485, total=   8.6s\n",
            "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
            "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=   9.0s\n",
            "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
            "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=   8.9s\n",
            "[CV] C=9.324426408004218, gamma=0.0026587543983272693 ................\n",
            "[CV] . C=9.324426408004218, gamma=0.0026587543983272693, total=   8.8s\n",
            "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
            "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=   8.7s\n",
            "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
            "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=   8.7s\n",
            "[CV] C=2.818249672071006, gamma=0.0023270677083837795 ................\n",
            "[CV] . C=2.818249672071006, gamma=0.0023270677083837795, total=   8.7s\n",
            "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
            "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=   8.8s\n",
            "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
            "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=   8.8s\n",
            "[CV] C=4.042422429595377, gamma=0.011207606211860567 .................\n",
            "[CV] .. C=4.042422429595377, gamma=0.011207606211860567, total=   8.9s\n",
            "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
            "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=   8.7s\n",
            "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
            "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=   8.8s\n",
            "[CV] C=5.319450186421157, gamma=0.003823475224675185 .................\n",
            "[CV] .. C=5.319450186421157, gamma=0.003823475224675185, total=   8.8s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Done  30 out of  30 | elapsed:  4.6min finished\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RandomizedSearchCV(cv=3, error_score=nan,\n",
              "                   estimator=SVR(C=1.0, cache_size=200, coef0=0.0, degree=3,\n",
              "                                 epsilon=0.1, gamma='scale', kernel='rbf',\n",
              "                                 max_iter=-1, shrinking=True, tol=0.001,\n",
              "                                 verbose=False),\n",
              "                   iid='deprecated', n_iter=10, n_jobs=None,\n",
              "                   param_distributions={'C': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fc799bbd780>,\n",
              "                                        'gamma': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fc799bbd630>},\n",
              "                   pre_dispatch='2*n_jobs', random_state=42, refit=True,\n",
              "                   return_train_score=False, scoring=None, verbose=2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MTGJLiAmRj-J",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "41b26037-b0eb-4d49-8ffc-3d77b94113d3"
      },
      "source": [
        "rnd_search_cv.best_estimator_"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVR(C=4.745401188473625, cache_size=200, coef0=0.0, degree=3, epsilon=0.1,\n",
              "    gamma=0.07969454818643928, kernel='rbf', max_iter=-1, shrinking=True,\n",
              "    tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3tyGLy-tRj-K",
        "colab_type": "text"
      },
      "source": [
        "Now let's measure the RMSE on the training set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KWLfmgC3Rj-L",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "27aa63a5-0df5-42aa-d14c-685491309320"
      },
      "source": [
        "y_pred = rnd_search_cv.best_estimator_.predict(X_train_scaled)\n",
        "mse = mean_squared_error(y_train, y_pred)\n",
        "np.sqrt(mse)"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5727524770785356"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "miFQFm9zRj-N",
        "colab_type": "text"
      },
      "source": [
        "Looks much better than the linear model. Let's select this model and evaluate it on the test set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3HK-EU7JRj-N",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "f2d8aa2d-5b2c-47b1-dcb3-dfc67d887eda"
      },
      "source": [
        "y_pred = rnd_search_cv.best_estimator_.predict(X_test_scaled)\n",
        "mse = mean_squared_error(y_test, y_pred)\n",
        "np.sqrt(mse)"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.592916838552874"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K4BUQ-ffRj-P",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 82,
      "outputs": []
    }
  ]
}